Firstly, it's not just in Asia, there are many other places that also have mathematics similar to Asia. and secondly, mathematics in America is actually quite easy, except in Brazil, which is difficult to understand in Brazil...
For people wondering about the mass of the sun (which is dead easy to calculate) Use kepler's third law (T^2 is proportional to a^3) T is the time that one full orbit takes A is the average distance between the sun and the earth (one astronomical unit, or approx. 150 000 000 000 metres) Now we can use Kepler's principle that 4pi^2/GM is equal to 1. This means that we can plug it into our other formula, creating T^2 = (4pi^2/GM)•(a^3) Now lets arrange the equation to make M the subject T^2 = (4pi^2/GM)•(a^3) T^2•M = (4pi^2/G)•(a^3) M = (4pi^2/G•T^2)•(a^3) Now we can plug in the values: We use metres for A, meaning A is approx. 150 000 000 000m We use seconds for T, meaning T is approx. (365•24•60•60)s G is the gravitational constant, or 6.67•10^-11 Pi is just pi, or 3.14159265 (thats all i remember) We plug in the values: M=(4•3.1415...^2/(365•24•60•60)^2•(6.67•10^-11))•(150000000000)^3 We unfortunately use a calculator because im not the "approximating 11+2" guy This equals to 2.0086•10^30 kg, which is indeed the mass of the sun! This is not entirely accurate as other planets affect the earth's orbit by moving the sun around (i forgot the scientific term for that) Also btw i didnt use google for this bc i learned this in school at 9th grade, the equation is pretty easy to remember Physics seems hard, but if you look at it the right way it becomes much easier
@@ISAIDALMONDTOFU No, thats not. We do divisiom like every another country, but the Brazillian on the video was just teaching a trick to solve it whit a simple form. Whe learn division like in the 3rd grade with 7/8 years
Explaination: 6! is 6 period which means 1x2x3x4x5x6 and then 4! is 1x2x3x4. which means 720 out of 24 which means u have to do 720/24 which equals to 30. (and i definitely didn't use calculator)
Welp, Atleast I found an Arab because everyone stereotypes Aisans as "China, Japan, Korea (there's north and South)" and forget about Syria, Iraq, Alaska (US state + Yes, If you count Some islands in the Pacific) Kazakhstan, Papua New Guinea, Uzbekistan and other.
American maths ❌️ Asian maths ❌️ European maths ✅️ (Calculus was discovered by Isaac Newton, from England, and the video shows Euler Formula, and Leonhard Euler was from Switzerland)
Давай разберем подробно: Шаг 1. Вспомним, что такое факториал. Факториал - это произведение всех натуральных чисел от 1 до . Например: Шаг 2. Как делить факториалы. Когда мы делим на , можно упростить выражение: \frac{6!}{4!} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1} Шаг 3. Сократим одинаковые множители. Числа находятся и в числителе, и в знаменателе, поэтому они сокращаются: \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1} = 6 \cdot 5 = 30 Ответ: \frac{6!}{4!} = 30 Так проще считать, потому что не нужно вычислять полные факториалы.
Middle School: I mean, this is still somewhat easy. Pi and x are still pretty hard, though. High School: WHAT THE HELL AM I LOOKING AT?! IT'S ALL LETTERS! IT'S ALL LETTERS!
Applies for europeans too, barely in 9th grade and my math teacher gave us this as homework: The surface area of a torus is given by: A = 4\pi^2 Rr, Prove this formula by parametrizing the torus in 3D space using: x(u, v) = (R + r \cos v) \cos u, \quad y(u, v) = (R + r \cos v) \sin u, \quad z(u, v) = r \sin v.
Don't even think about it bro, this vid is made by Indian and made for Indian. They have such a big ego that videos like these have a lot of views and likes
Cap fr calculus can't be taught so early from linear equations atleast 5-6 yrs mastery in linear equations. And calculus canbe learnt in 2-3+college(if ur not only learning basic integration and differentiation) years
As an Person who went to Asia before we learned this Basic Operations 1. + (Plus): Addition. 2. − (Minus): Subtraction. 3. × (Times): Multiplication. 4. ÷ (Divided by): Division. 5. = (Equals): Equality. 6. ≠ (Not equal to): Inequality. 7. ≈ (Approximately equal to): Approximate equality. 8. < (Less than): Less than. 9. > (Greater than): Greater than. 10. ≤ (Less than or equal to): Less than or equal to. 11. ≥ (Greater than or equal to): Greater than or equal to. 12. ∞ (Infinity): Infinite value. Set Operations 13. ∈ (Element of): Belongs to a set. 14. ∉ (Not an element of): Does not belong to a set. 15. ⊂ (Subset): A subset of a set. 16. ⊆ (Subset or equal to): Subset or equal to. 17. ⊄ (Not a subset): Not a subset. 18. ∪ (Union): Union of sets. 19. ∩ (Intersection): Intersection of sets. 20. ∅ (Empty set): The empty set. 21. \ (Set difference): Difference between sets. 22. △ (Symmetric difference): Symmetric difference between two sets. 23. ⊃ (Superset): A superset of a set. 24. ⊇ (Superset or equal to): Superset or equal to. 25. ⊥ (Perpendicular): Perpendicular lines. 26. ∥ (Parallel): Parallel lines. 27. ⊥ (Non-parallel): Non-parallel lines. Logical Operators 28. ∧ (Logical AND): Logical conjunction (and). 29. ∨ (Logical OR): Logical disjunction (or). . EDIT: you will learn this from grade 7 to grade 11 or 12 cause i'm at grade 10 and in grade 11 we will learn about π the words like in grade 8 we learned about Slope. So it was hard for Me Edit: (again) if you like to know the symbols π is a greek letter edit: i didnt have time to add the rest so there it is 9. ∨ (Logical OR): Logical disjunction (or). 30. ¬ (Negation): Logical negation. 31. ⇒ (Implies): Logical implication. 32. ⇔ (If and only if): Logical equivalence. 33. ⊕ (Exclusive OR or XOR): Exclusive or, logical operator. 34. ∝ (Proportional to): Proportionality. 35. ∀ (Universal quantifier): For all. 36. ∃ (Existential quantifier): There exists. 37. ∄ (There does not exist): There does not exist. 38. ∃! (Uniqueness quantifier): There exists exactly one. 39. ⊤ (True): Represents true in logic. 40. ⊥ (False): Represents false in logic. Arithmetic and Algebraic Symbols 41. ± (Plus-minus sign): Plus or minus. 42. ∓ (Minus-plus sign): Minus or plus. 43. |x| (Absolute value): The absolute value of x. 44. ∑ (Summation): Sum of terms. 45. ∏ (Product): Product of terms. 46. √ (Square root): Square root of a number. 47. ∛ (Cube root): Cube root of a number. 48. ! (Factorial): Factorial, e.g., 5! = 5 × 4 × 3 × 2 × 1. 49. x! (Factorial): The product of all positive integers up to x. 50. xₙ (Binomial coefficient): - used to calculate combinations. 51. f(x) (Function): A function of x. 52. f∘g (Function composition): The composition of functions f and g. 53. log (Logarithm): The logarithm of a number. Constants and Special Numbers 54. π (Pi): The ratio of a circle’s circumference to its diameter. 55. e (Euler’s number): The base of natural logarithms, approximately 2.718. 56. τ (Tau): 2π, a constant used in some circles. 57. ℵ₀ (Aleph-null): Cardinality of the set of natural numbers (countable infinity). 58. ℵ₁ (Aleph-one): Cardinality of the continuum (real numbers). 59. γ (Gamma): The Euler-Mascheroni constant. 60. φ (Phi): The golden ratio, approximately 1.618. 61. ℱ (Fraktur F): Often used to represent Fourier transforms or fields. 62. ζ (Zeta): Used in the Riemann zeta function. 63. μ (Mu): Used in statistics for mean, or in physics for permeability. 64. σ (Sigma): Standard deviation, or summation notation. 65. λ (Lambda): Eigenvalues in linear algebra or wavelength in physics. 66. κ (Kappa): Curvature or a constant in various contexts. 67. ϕ (Phi): Used for potential functions, golden ratio. 68. ℝ (Real numbers): The set of real numbers. 69. ℂ (Complex numbers): The set of complex numbers. 70. ℍ (Quaternions): The set of quaternions. 71. ℙ (Prime numbers): The set of prime numbers. Functions and Notation 72. f'(x) (Newton’s notation): The first derivative of f at x. 73. f''(x) (Newton’s notation): The second derivative of f at x. 74. D (Leibniz’s notation): Used to denote the derivative. 75. (Leibniz’s notation): Leibniz’s notation for the derivative. 76. L(x) (Lagrange’s function): A notation for a function in calculus or mechanics. Fraction and Decimal Notations 77. x/y (Fraction): Division expressed as a fraction. 78. ẋ (Decimal notation): Decimal representation or repeating decimals. 79. ⌊x⌋ (Floor function): The greatest integer less than or equal to x. 80. ⌈x⌉ (Ceiling function): The least integer greater than or equal to x. 81. [x] (Nearest integer function): The nearest integer to x. Blackboard Bold Typeface 82. ℕ (Natural numbers): The set of natural numbers. 83. ℤ (Integers): The set of integers. 84. ℚ (Rational numbers): The set of rational numbers. 85. ℝ (Real numbers): The set of real numbers. 86. ℂ (Complex numbers): The set of complex numbers. 87. ℍ (Quaternions): The set of quaternions. Miscellaneous 88. # (Number sign): Often used for "hashtag," but also for denoting "number" in certain contexts. 89. → (Right arrow): Indicates direction or mapping. 90. ← (Left arrow): Indicates direction. 91. ↔ (Double arrow): Represents equivalence or bi-directional relationship. Floor and Ceiling Functions 92. ⌊x⌋ (Floor): The greatest integer less than or equal to x. 93. ⌈x⌉ (Ceiling): The least integer greater than or equal to x. --- 50 Important Constants 1. π: 3.14159… (Circumference to diameter ratio in a circle). 2. e: 2.71828… (Euler's number, base of natural logarithms). 3. φ: 1.61803… (Golden ratio). 4. i: √-1 (Imaginary unit). 5. ℵ₀: The cardinality of the set of natural numbers (countable infinity). 6. ℵ₁: The cardinality of the continuum (real numbers). 7. γ: 0.57721… (Euler-Mascheroni constant). 8. τ: 6.28318… (2π, in some mathematical contexts preferred over π). 9. log₂: Logarithm base 2. 10. log₁₀: Logarithm base 10 (common logarithm). 11. √2: 1.41421… (Square root of 2). 12. √3: 1.73205… (Square root of 3). 13. √5: 2.23607… (Square root of 5). 14. 1/137: The fine-structure constant. 15. G: 6.67430 × 10⁻¹¹ (Gravitational constant). 16. c: 3 × 10⁸ (Speed of light in vacuum). 17. k: 1.38065 × 10⁻²³ (Boltzmann constant). 18. h: 6.62607015 × 10⁻³⁴ (Planck's constant). 19. α: 0.007297 (Fine-structure constant). 20. β: Often used for a coefficient in physics. 21. µ: 1.256637061 × 10⁻⁶ (Magnetic permeability). 22. ε₀: 8.854 × 10⁻¹² (Electric constant). 23. ℘: Used for the Weierstrass elliptic function. 24. d: 9.80665 (Acceleration due to gravity on Earth). 25. Z₀: The characteristic impedance of free space. 26. R₀: Reproduction number (epidemiology). 27. L₀: The cosmological constant in physics. 28. π₀: A particle in physics (Pion). 29. θ₀: Initial angle in trigonometry. 30. ρ₀: The density of a substance at reference conditions. 31. S₀: The entropy at the reference temperature. 32. τ₀: Relaxation time in physics. 33. ν₀: The frequency of oscillation in physics. 34. ξ₀: The initial value of a variable in physics. 35. χ₀: Magnetic susceptibility. 36. μ₀: Magnetic constant (permeability). 37. ℑ (Imaginary part): Part of a complex number. 38. ℜ (Real part): Real part of a complex number. 39. Ω: 8.6173 × 10⁻⁵ (Boltzmann constant in electron volts per Kelvin). 40. λ: Wavelength in physics. 41. σ: Stefan-Boltzmann constant. 42. p: The pressure of a system. 43. n₀: Index of refraction. 44. z₀: Distance scale factor in physics. 45. K₀: A constant in thermodynamics or physics. 46. M₀: Initial mass in physics. 47. A₀: The initial area or cross-section. 48. b₀: The initial magnetic field strength. 49. T₀: Reference temperature in thermodynamics. 50. F₀: The initial force applied. ∼ (tilde): Generally used to denote an equivalence relation. For example, a ∼ b a∼b usually means that a a is equivalent to b b in some sense (like in the context of congruence modulo some relation). ≅ (cong): This symbol is commonly used to denote an isomorphism between two objects. For instance, A ≅ B A≅B indicates that A A and B B are isomorphic, meaning there is a morphism between them that has an inverse, establishing a one-to-one correspondence. ≃ (simeq): Typically used to denote a weaker notion of equivalence, such as homotopy equivalence in algebraic topology. That is, A ≃ B A≃B suggests that A A and B B can be continuously transformed into one another. ≈ (approx): This symbol often signifies an approximate equivalence rather than a strict one. It might be used in contexts where an entity can be considered "close to" another, such as in analysis or when discussing asymptotic behavior.
This ain't always true. Well maybe if you ain't a math profession but if you're, this is entirely flawed and context dependant. Different symbols mean different things depending on the context and different writers use different notations even in the same context if you continue studying in abstract math. For example, the logical operator "and" is usually used for the wedge products, "×" can be used for a lot other things as well like product spaces, and the non parallel symbol can also be used for different things in wheel theory
@@like_that4966 i understand what do you mean even tho i'm not that close of being a math profession "×" which before i thought it was 100% useless for me until i realized it can make products and other things i can see . thank you help about the "×"
@hungary-v9o Ya, there are a lot more, pretty much all and the symbols are never standard for any and always context dependant. For more example amoung extremely many, π can also be used to denote prime counting function or homotopy groups. And we don't always use i to denote the imaginary unit, I saw j being used to denote it back in Fourier analysis. And the symbol for exclusive or actually is more commonly used for direct sums somehow. You also didn't mention the symbol for tensor products, they're real cool ngl.And a lot of the constants are from physics. There are a lot more u missed too, most noticeably the symbols for morphisms.
@@like_that4966 Ya the reason of the symbol of tensor we didn't learn about it even π that we got homework to say 50 π words , anyway the "u missed too, most noticeably the symbols for morphisms" i will try my best to understand the symbol for morphisms to in like a short while i will prob do it cause i got to do research some u missed too, most noticeably the symbols for morphisms. letter then ill add the 2 things you said cause i'm researching them. the most sufferage thing i got on was find the "×" and (A²+B²)=A²+2AB+B²) and in grade 8 is slope.
Ah yes, I haven’t had these type of equations, but for now I have Algebra 1 as a sort of “challenging” question similar to these: 6N-5=35 3+4N=27 3N+4=16 9-7N=-54
"Gopal is going on a car at 300 km/h, there's a truck coming right in front of him at *x* km/h, calculate the: 1. Initial velocity. 2. Final velocity. 3. Probability of him dying right under the truck."
Newton's work spans various fields, including physics and mathematics, and has produced several well-known formulas. Here are some key formulas associated with Sir Isaac Newton: 1. Newton's Laws of Motion: First Law (Law of Inertia): \text{An object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force.} Second Law (F = ma): F = ma - F is the force applied, - m is the mass of the object, - a is the acceleration of the object. Third Law (Action and Reaction): F_{12} = - F_{21} 2. Newton's Law of Universal Gravitation: F = G \frac{m_1 m_2}{r^2} is the gravitational force between two masses, is the gravitational constant, and are the masses of the two objects, is the distance between their centers. 3. Newton's General Binomial Theorem (Binomial Expansion): For any real number and : (1 + x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \cdots 4. Newton's Forward Difference Formula (Interpolation): If is a function with values at equally spaced points, the forward difference formula for approximation is: f(x_0 + h) \approx f(x_0) + \Delta f(x_0) + \frac{\Delta^2 f(x_0)}{2!} + \cdots 5. Newton's Method (Root-Finding Algorithm): Newton's method is used to approximate the roots of a function. The formula is: x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} is the current guess, is the function evaluated at , is the derivative of the function at . 6. Newton-Cotes Formula (Numerical Integration): This family of formulas provides a way to approximate the integral of a function. One common example is the trapezoidal rule, which is a simple case of the Newton-Cotes method: \int_a^b f(x) \, dx \approx \frac{b - a}{2} (f(a) + f(b)) These are some of the most important formulas linked to Newton's contributions to science and mathematics. Let me know if you'd like a deeper explanation of any specific formula.
/w oldwokefan1 This requirement is presentated in the Harvard Website its selves English Proficiency Requirement Applicants who are non-native English speakers can demonstrate English proficiency in one of three ways: Receiving an undergraduate degree from an academic institution where English is the primary language of instruction. Earning a minimum score of 80 on the internet based test (iBT) of the Test of English as a Foreign Language (TOEFL)* Earning a minimum score of 6.5 on the International English Language Testing System (IELTS) Academic test.* Harvard strongly recommends Over 4 years of english with a strong writing component
@Oldwokenfan1 That was completly unnecesary input. I pasted those exactly from it's source Being the Harvard websites its selves. Alright Maybe he does'nt gave shit About it.
Ok guys, imma turn into a teacher rq.. PEMDAS. (4 operations) 10×(10÷2)+20-3 How do you solve it? P - Parenthesis E - Exponent (mostly not in solving) M - Multiplication D - Division A - Addition S - Subtract To solve 10×(10÷2)+20-3, the parenthesis/numbers in the brackets should be solved first. 10 divided by 2 is equal to 5. So, 10 divided by 5 is equal to 2. Theres no exponent, so lets move on to adding. 2 plus 20 is equal to 22. Onto subracting, 22-3 is equal to 19. Therefore, the final answer is "19". Sol: 10×(10÷2)+20-3 =2+20-3 =22-3 ="19" Tbh in my classroom they say its easy
Imagine paper of ISI Maths India ☠️☠️ Your university professors can’t solve every question of this paper and the paper is given by 16-17yr old students ☠️☠️ Just search paper of ISI Maths Chennai India =☠️
who the hell said creators of maths were arabs mainly it devloped in china,india,greek and egypt and also calclus was devloped by newton one of the most important devlopment were done by these civilisation not arabs
thats normal bruv i now all areas all volumes fibonacci. arithmethic equation and the uh (sorry i dont understand this in english) but like the Un and Sn method then the ratio Un and Sn method. Combinatorics then cryptharithm then phytagoras then fibonacci. Lcm and that one other. And many more
The man on the upper vídeo IS NOT AMERICAN, he is Brazilian, his RUclips channel name is "Professor Mr.Bean" Since his appearance is a lot like Mr. Bean's he chose this name. His classes are very cool btw🙃
Let’s write a list from 1-2000: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000
American math vs Asian math❌
Middle school vs high school✅
This aint math anymore this is idk
That's grade 7-11 math@@zaynandysequel
Fr bro
i wasn’t taught about factorials in middle school lol
the only reason why i know about them is the internet
"Low school - High school
Asian Maths: proceeds to show images of american and european scientists
Ramanujan and Indian Scientists laughing in the corner 😂
@@theresponsibleuser90fr✊
Math originated in the middle East-Asia
@@theresponsibleuser90 i am not talking about science, i am talking about the video😭😭😭
@@warsolos i am not talking about science, i am talking about the video😭😭😭
As an asian student.I HATE
(A²+B²)=A²+2AB+B²
(A-B)²=A²-2AB+B²
A²-B²=(A+B)×(A-C)
(A+B)³=A³+3A²B+3AB²+B³
(A-B)³=A³-3A²B+3AB²-B³
Pascals triangle is underrated af
bruh this is the easiest among many things in asia
As a pakistani student, real.
Dude for real these are easier ones than the Pythagorean theorum ☠️
What formula is that, stop if you don’t know maths.
We got Mr. Bean as my math teacher before GTA six
he is already genius but he chosed a job he want
Amercan school 😏 skip
Asian school: try me 💀💀
Firstly, it's not just in Asia, there are many other places that also have mathematics similar to Asia.
and secondly, mathematics in America is actually quite easy, except in Brazil, which is difficult to understand in Brazil...
The guy in the video above is from Brazil
Not really In Brazil And in America it depends.
In Europe it's also difficult (at least in my country)
Peru is also hard, for some reason they won some maths tournaments in Latin America
As a brazilian i don't think so
For people wondering about the mass of the sun (which is dead easy to calculate)
Use kepler's third law (T^2 is proportional to a^3)
T is the time that one full orbit takes
A is the average distance between the sun and the earth (one astronomical unit, or approx. 150 000 000 000 metres)
Now we can use Kepler's principle that 4pi^2/GM is equal to 1.
This means that we can plug it into our other formula, creating T^2 = (4pi^2/GM)•(a^3)
Now lets arrange the equation to make M the subject
T^2 = (4pi^2/GM)•(a^3)
T^2•M = (4pi^2/G)•(a^3)
M = (4pi^2/G•T^2)•(a^3)
Now we can plug in the values:
We use metres for A, meaning A is approx. 150 000 000 000m
We use seconds for T, meaning T is approx. (365•24•60•60)s
G is the gravitational constant, or 6.67•10^-11
Pi is just pi, or 3.14159265 (thats all i remember)
We plug in the values:
M=(4•3.1415...^2/(365•24•60•60)^2•(6.67•10^-11))•(150000000000)^3
We unfortunately use a calculator because im not the "approximating 11+2" guy
This equals to 2.0086•10^30 kg, which is indeed the mass of the sun!
This is not entirely accurate as other planets affect the earth's orbit by moving the sun around (i forgot the scientific term for that)
Also btw i didnt use google for this bc i learned this in school at 9th grade, the equation is pretty easy to remember
Physics seems hard, but if you look at it the right way it becomes much easier
Easy 💀
Approximating guy😂😂
Quite light
Thats not easy
What the
American Maths ✅
A Brazilian teacher trying to teach division ❌
Brazillian is a South America country
@Systemizando But I put America because it's the United States or Americans
But that Guy is Brazilian@@isisrafaela2466
That’s how they do division in Brazil? Ah, ok, we do multiplication in 3rd grade and we start division at the start of 4th grade in the Philippines
@@ISAIDALMONDTOFU No, thats not. We do divisiom like every another country, but the Brazillian on the video was just teaching a trick to solve it whit a simple form. Whe learn division like in the 3rd grade with 7/8 years
Explaination: 6! is 6 period which means 1x2x3x4x5x6 and then 4! is 1x2x3x4. which means 720 out of 24 which means u have to do 720/24 which equals to 30. (and i definitely didn't use calculator)
And 9! Is 362 880. I DIDN'T USE CALCULATOR
You can calculate the answer of 6!/4! By just 6x5
Just like
4!=4x3x2x1 or 1x2x3x4=am lazy
2!=2x1=2
We can just do 4x3 and yep, 12
I aint reading all that
6 factorial
11th class question lol
as an asian student,this is so true.
Welp, Atleast I found an Arab because everyone stereotypes Aisans as "China, Japan, Korea (there's north and South)" and forget about Syria, Iraq, Alaska (US state + Yes, If you count Some islands in the Pacific) Kazakhstan, Papua New Guinea, Uzbekistan and other.
Agreed
@@Tinfoils-negotiationalaska is in north America
@@Tinfoils-negotiationpacific isalands and New Guinea is a part of oceania
In Poland those are "Basics" [Nothing basic about that sh-]
As an Asian our teacher gave us homework to calculate the mass of the sun.
Bro thats literally cap
@@FD_Edits567can't you take a joke
i actually got this a few months ago fucking insane@@FD_Edits567
@@FD_Edits567 chill bro it's just a joke
But sometimes math is hard
“This man is a mathematical genius, he just doesn’t know it yet” ahh sound 💀💀
Whats the song name? (Its not definitely Memory Reboot Slowed)
Life letters- never get used to people is song name
@notfoundeditz0 W man
@@Woohoo6789 W
@@notfoundeditz0 W
@@notfoundeditz0W
As an Asian student, its so true
Have you ever tried American schools?
As an American Student this is so not true.
American maths ❌️
Asian maths ❌️
European maths ✅️ (Calculus was discovered by Isaac Newton, from England, and the video shows Euler Formula, and Leonhard Euler was from Switzerland)
American math vs Asian math❌
Worldwide math vs worldwide math✅
Yea
Давай разберем подробно:
Шаг 1. Вспомним, что такое факториал.
Факториал - это произведение всех натуральных чисел от 1 до . Например:
Шаг 2. Как делить факториалы.
Когда мы делим на , можно упростить выражение:
\frac{6!}{4!} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1}
Шаг 3. Сократим одинаковые множители.
Числа находятся и в числителе, и в знаменателе, поэтому они сокращаются:
\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1} = 6 \cdot 5 = 30
Ответ:
\frac{6!}{4!} = 30
Так проще считать, потому что не нужно вычислять полные факториалы.
As a asian average child I can confirm that I learn this all shit my my mothers womb...
It's true that we are burdened with mathematics very heavily... In America or in the USA simplified mathematics
What is the original math edit i want to see it full screen.
Triangle congruency might be easier than i expected
I'm learning traingles right now
Primary school: yo this is pretty easy
Middle school: PAIN
High school: please end my suffering
Middle School: I mean, this is still somewhat easy. Pi and x are still pretty hard, though.
High School: WHAT THE HELL AM I LOOKING AT?! IT'S ALL LETTERS! IT'S ALL LETTERS!
Middle school ain't shit
You play Roblox lil bro, get life
As an Asian student (Iranian) its so true
It has nothing to do with Asia or Iran
@CypherInfintie I don't know but I think for example if Americans learn something in 10 th grade Asians learn it on 8 th grade
I'm not sure
@CypherInfintie I said only I'm from Iran
@CypherInfintie say something
Applies for europeans too, barely in 9th grade and my math teacher gave us this as homework:
The surface area of a torus is given by:
A = 4\pi^2 Rr,
Prove this formula by parametrizing the torus in 3D space using:
x(u, v) = (R + r \cos v) \cos u, \quad y(u, v) = (R + r \cos v) \sin u, \quad z(u, v) = r \sin v.
Its a sin
@@乙乙乙乙乙乙乙乙乙乙 I know
As an 8th grader I'm now traumatize-
Me too
How old? 15?
The stuff up top is like basic trigonometry and a little bit of calculus. Idk why people think it’s super difficult
This is funny because all of the scientists/mathematicians shown on the asian side were american
Don't even think about it bro, this vid is made by Indian and made for Indian. They have such a big ego that videos like these have a lot of views and likes
European
As an Indian i agree@@razafg
european**
@@razafgyeah probably
“Yeah just a little difference”💀
Still easier to handle from what im having next week 😅
Asian maths ❌
Maths for asian students ✅
Türkiye maths: 💀☠️🗿💥💥
Sen sadece sevmiyorsun olm
You literally watch skibpitty dob dob yes
Memory Reboot is sounding different shit right now
Which Asia?
China, India,korea
Don't Forget Japan, Russia, Iran, UAE, Armenia, Thailand and Many More.
Insect eater, scam center and Desert oil
South Asia
Azerbaijan we are learning very hard math btw
American maths vs Asian maths: ✖️
American Middle School math: World Wide math
The guy on american is Brazilian
Yes, he is, America is a continent, Brazil is on South America
I love when we use alphabet in Math, like bru tf is ( A²+B³ ) - A³ + B³ + ( A³ - B² ) and im in goddamn seventh grade
Bro really said "Just a little difference " ☠️☠️☠️☠️
He did NOT say that
Y intercept of the y axis= (y,y)
Linear equations in grade 5 and calculus at 7 is what i was taught
Cap fr calculus can't be taught so early from linear equations atleast 5-6 yrs mastery in linear equations. And calculus canbe learnt in 2-3+college(if ur not only learning basic integration and differentiation) years
You probably think linear equations is expressions or shi and calculus is finding area
It's not cap he or she is right in Pakistan as well not everything is cap go search it on Google we were tought that before you guys.
That's what am thinking😂@@aarohan1184
Cap bro almost everyone learns linear equations in 7th grade then after that is just precalculus, you get to learn basic calc at 10th or 11th grade
As an Asian, I can't confirm
Do any of you know the name of the song?
Life letters never get used to people's
Romanian Maths:136-x789c&92
4562-67-975-b67k=-206.15 °C
5667-99-9-0.9
XY75-2281I-x1x1x1
7626-45-960-6b
b8b8k-b9o8sh8a
20=51=P5≈E5
Original of the Asians math video?
"it all starts from X in 6th grade"
The delta dance was insane.
As an Person who went to Asia before we learned this Basic Operations
1. + (Plus): Addition.
2. − (Minus): Subtraction.
3. × (Times): Multiplication.
4. ÷ (Divided by): Division.
5. = (Equals): Equality.
6. ≠ (Not equal to): Inequality.
7. ≈ (Approximately equal to): Approximate equality.
8. < (Less than): Less than.
9. > (Greater than): Greater than.
10. ≤ (Less than or equal to): Less than or equal to.
11. ≥ (Greater than or equal to): Greater than or equal to.
12. ∞ (Infinity): Infinite value.
Set Operations
13. ∈ (Element of): Belongs to a set.
14. ∉ (Not an element of): Does not belong to a set.
15. ⊂ (Subset): A subset of a set.
16. ⊆ (Subset or equal to): Subset or equal to.
17. ⊄ (Not a subset): Not a subset.
18. ∪ (Union): Union of sets.
19. ∩ (Intersection): Intersection of sets.
20. ∅ (Empty set): The empty set.
21. \ (Set difference): Difference between sets.
22. △ (Symmetric difference): Symmetric difference between two sets.
23. ⊃ (Superset): A superset of a set.
24. ⊇ (Superset or equal to): Superset or equal to.
25. ⊥ (Perpendicular): Perpendicular lines.
26. ∥ (Parallel): Parallel lines.
27. ⊥ (Non-parallel): Non-parallel lines.
Logical Operators
28. ∧ (Logical AND): Logical conjunction (and).
29. ∨ (Logical OR): Logical disjunction (or).
. EDIT: you will learn this from grade 7 to grade 11 or 12 cause i'm at grade 10 and in grade 11 we will learn about π the words like in grade 8 we learned about Slope. So it was hard for Me Edit: (again) if you like to know the symbols π is a greek letter edit: i didnt have time to add the rest so there it is 9. ∨ (Logical OR): Logical disjunction (or).
30. ¬ (Negation): Logical negation.
31. ⇒ (Implies): Logical implication.
32. ⇔ (If and only if): Logical equivalence.
33. ⊕ (Exclusive OR or XOR): Exclusive or, logical operator.
34. ∝ (Proportional to): Proportionality.
35. ∀ (Universal quantifier): For all.
36. ∃ (Existential quantifier): There exists.
37. ∄ (There does not exist): There does not exist.
38. ∃! (Uniqueness quantifier): There exists exactly one.
39. ⊤ (True): Represents true in logic.
40. ⊥ (False): Represents false in logic.
Arithmetic and Algebraic Symbols
41. ± (Plus-minus sign): Plus or minus.
42. ∓ (Minus-plus sign): Minus or plus.
43. |x| (Absolute value): The absolute value of x.
44. ∑ (Summation): Sum of terms.
45. ∏ (Product): Product of terms.
46. √ (Square root): Square root of a number.
47. ∛ (Cube root): Cube root of a number.
48. ! (Factorial): Factorial, e.g., 5! = 5 × 4 × 3 × 2 × 1.
49. x! (Factorial): The product of all positive integers up to x.
50. xₙ (Binomial coefficient): - used to calculate combinations.
51. f(x) (Function): A function of x.
52. f∘g (Function composition): The composition of functions f and g.
53. log (Logarithm): The logarithm of a number.
Constants and Special Numbers
54. π (Pi): The ratio of a circle’s circumference to its diameter.
55. e (Euler’s number): The base of natural logarithms, approximately 2.718.
56. τ (Tau): 2π, a constant used in some circles.
57. ℵ₀ (Aleph-null): Cardinality of the set of natural numbers (countable infinity).
58. ℵ₁ (Aleph-one): Cardinality of the continuum (real numbers).
59. γ (Gamma): The Euler-Mascheroni constant.
60. φ (Phi): The golden ratio, approximately 1.618.
61. ℱ (Fraktur F): Often used to represent Fourier transforms or fields.
62. ζ (Zeta): Used in the Riemann zeta function.
63. μ (Mu): Used in statistics for mean, or in physics for permeability.
64. σ (Sigma): Standard deviation, or summation notation.
65. λ (Lambda): Eigenvalues in linear algebra or wavelength in physics.
66. κ (Kappa): Curvature or a constant in various contexts.
67. ϕ (Phi): Used for potential functions, golden ratio.
68. ℝ (Real numbers): The set of real numbers.
69. ℂ (Complex numbers): The set of complex numbers.
70. ℍ (Quaternions): The set of quaternions.
71. ℙ (Prime numbers): The set of prime numbers.
Functions and Notation
72. f'(x) (Newton’s notation): The first derivative of f at x.
73. f''(x) (Newton’s notation): The second derivative of f at x.
74. D (Leibniz’s notation): Used to denote the derivative.
75. (Leibniz’s notation): Leibniz’s notation for the derivative.
76. L(x) (Lagrange’s function): A notation for a function in calculus or mechanics.
Fraction and Decimal Notations
77. x/y (Fraction): Division expressed as a fraction.
78. ẋ (Decimal notation): Decimal representation or repeating decimals.
79. ⌊x⌋ (Floor function): The greatest integer less than or equal to x.
80. ⌈x⌉ (Ceiling function): The least integer greater than or equal to x.
81. [x] (Nearest integer function): The nearest integer to x.
Blackboard Bold Typeface
82. ℕ (Natural numbers): The set of natural numbers.
83. ℤ (Integers): The set of integers.
84. ℚ (Rational numbers): The set of rational numbers.
85. ℝ (Real numbers): The set of real numbers.
86. ℂ (Complex numbers): The set of complex numbers.
87. ℍ (Quaternions): The set of quaternions.
Miscellaneous
88. # (Number sign): Often used for "hashtag," but also for denoting "number" in certain contexts.
89. → (Right arrow): Indicates direction or mapping.
90. ← (Left arrow): Indicates direction.
91. ↔ (Double arrow): Represents equivalence or bi-directional relationship.
Floor and Ceiling Functions
92. ⌊x⌋ (Floor): The greatest integer less than or equal to x.
93. ⌈x⌉ (Ceiling): The least integer greater than or equal to x.
---
50 Important Constants
1. π: 3.14159… (Circumference to diameter ratio in a circle).
2. e: 2.71828… (Euler's number, base of natural logarithms).
3. φ: 1.61803… (Golden ratio).
4. i: √-1 (Imaginary unit).
5. ℵ₀: The cardinality of the set of natural numbers (countable infinity).
6. ℵ₁: The cardinality of the continuum (real numbers).
7. γ: 0.57721… (Euler-Mascheroni constant).
8. τ: 6.28318… (2π, in some mathematical contexts preferred over π).
9. log₂: Logarithm base 2.
10. log₁₀: Logarithm base 10 (common logarithm).
11. √2: 1.41421… (Square root of 2).
12. √3: 1.73205… (Square root of 3).
13. √5: 2.23607… (Square root of 5).
14. 1/137: The fine-structure constant.
15. G: 6.67430 × 10⁻¹¹ (Gravitational constant).
16. c: 3 × 10⁸ (Speed of light in vacuum).
17. k: 1.38065 × 10⁻²³ (Boltzmann constant).
18. h: 6.62607015 × 10⁻³⁴ (Planck's constant).
19. α: 0.007297 (Fine-structure constant).
20. β: Often used for a coefficient in physics.
21. µ: 1.256637061 × 10⁻⁶ (Magnetic permeability).
22. ε₀: 8.854 × 10⁻¹² (Electric constant).
23. ℘: Used for the Weierstrass elliptic function.
24. d: 9.80665 (Acceleration due to gravity on Earth).
25. Z₀: The characteristic impedance of free space.
26. R₀: Reproduction number (epidemiology).
27. L₀: The cosmological constant in physics.
28. π₀: A particle in physics (Pion).
29. θ₀: Initial angle in trigonometry.
30. ρ₀: The density of a substance at reference conditions.
31. S₀: The entropy at the reference temperature.
32. τ₀: Relaxation time in physics.
33. ν₀: The frequency of oscillation in physics.
34. ξ₀: The initial value of a variable in physics.
35. χ₀: Magnetic susceptibility.
36. μ₀: Magnetic constant (permeability).
37. ℑ (Imaginary part): Part of a complex number.
38. ℜ (Real part): Real part of a complex number.
39. Ω: 8.6173 × 10⁻⁵ (Boltzmann constant in electron volts per Kelvin).
40. λ: Wavelength in physics.
41. σ: Stefan-Boltzmann constant.
42. p: The pressure of a system.
43. n₀: Index of refraction.
44. z₀: Distance scale factor in physics.
45. K₀: A constant in thermodynamics or physics.
46. M₀: Initial mass in physics.
47. A₀: The initial area or cross-section.
48. b₀: The initial magnetic field strength.
49. T₀: Reference temperature in thermodynamics.
50. F₀: The initial force applied.
∼ (tilde): Generally used to denote an equivalence relation. For example,
a
∼
b
a∼b usually means that
a
a is equivalent to
b
b in some sense (like in the context of congruence modulo some relation).
≅ (cong): This symbol is commonly used to denote an isomorphism between two objects. For instance,
A
≅
B
A≅B indicates that
A
A and
B
B are isomorphic, meaning there is a morphism between them that has an inverse, establishing a one-to-one correspondence.
≃ (simeq): Typically used to denote a weaker notion of equivalence, such as homotopy equivalence in algebraic topology. That is,
A
≃
B
A≃B suggests that
A
A and
B
B can be continuously transformed into one another.
≈ (approx): This symbol often signifies an approximate equivalence rather than a strict one. It might be used in contexts where an entity can be considered "close to" another, such as in analysis or when discussing asymptotic behavior.
This ain't always true. Well maybe if you ain't a math profession but if you're, this is entirely flawed and context dependant. Different symbols mean different things depending on the context and different writers use different notations even in the same context if you continue studying in abstract math. For example, the logical operator "and" is usually used for the wedge products, "×" can be used for a lot other things as well like product spaces, and the non parallel symbol can also be used for different things in wheel theory
@@like_that4966 i understand what do you mean even tho i'm not that close of being a math profession "×" which before i thought it was 100% useless for me until i realized it can make products and other things i can see . thank you help about the "×"
@hungary-v9o Ya, there are a lot more, pretty much all and the symbols are never standard for any and always context dependant. For more example amoung extremely many, π can also be used to denote prime counting function or homotopy groups. And we don't always use i to denote the imaginary unit, I saw j being used to denote it back in Fourier analysis. And the symbol for exclusive or actually is more commonly used for direct sums somehow. You also didn't mention the symbol for tensor products, they're real cool ngl.And a lot of the constants are from physics. There are a lot more u missed too, most noticeably the symbols for morphisms.
Theres.. MORE?? 😭 😭
@@like_that4966 Ya the reason of the symbol of tensor we didn't learn about it even π that we got homework to say 50 π words , anyway the "u missed too, most noticeably the symbols for morphisms" i will try my best to understand the symbol for morphisms to in like a short while i will prob do it cause i got to do research some u missed too, most noticeably the symbols for morphisms. letter then ill add the 2 things you said cause i'm researching them. the most sufferage thing i got on was find the "×"
and (A²+B²)=A²+2AB+B²) and in grade 8 is slope.
Ah yes, I haven’t had these type of equations, but for now I have Algebra 1 as a sort of “challenging” question similar to these:
6N-5=35
3+4N=27
3N+4=16
9-7N=-54
Soon you'll get stuff like
8x+33=2x+9
Bro song??
Memory reboot (slowed)
Life letters
Life Letters (ultra slowed?
@@RGOGamerzno
This is actually true, the maths are extremely difficult in here
I think the real crime here is him using a decimal point as a multiplication sign
He isn't actually American, so he don't uses the . as the decimal point
The decimal point for the multiplication sign should be on the top not bottom to
Asian maths with this music looks like analog horror ✋🌈🤚
Bro why are the pages written in italian dude.. ( asian maths )
IM ITALIAN IM SO COOKED..
pretty sure most of the world would have the same maths just depends on the country you live in
Y'all mostly play "1.e4 Nf4 Bc4" right?
"Gopal is going on a car at 300 km/h, there's a truck coming right in front of him at *x* km/h, calculate the:
1. Initial velocity.
2. Final velocity.
3. Probability of him dying right under the truck."
Asian math ❌️
7 grade through 11 grade math✅️
Asia’s math 📊: solving for 'x'
America’s math 🧮: solving for snacks 🍟😂
"x" doesn't stand for "snacks". But Asians eat insects as snacks
memory reboot be sounding different today
Can u pls tell me the original song?
@@lol-n7e life letters.
Europe math: That stickman animation
Newton's work spans various fields, including physics and mathematics, and has produced several well-known formulas. Here are some key formulas associated with Sir Isaac Newton:
1. Newton's Laws of Motion:
First Law (Law of Inertia):
\text{An object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force.}
Second Law (F = ma):
F = ma
- F is the force applied,
- m is the mass of the object,
- a is the acceleration of the object.
Third Law (Action and Reaction):
F_{12} = - F_{21}
2. Newton's Law of Universal Gravitation:
F = G \frac{m_1 m_2}{r^2}
is the gravitational force between two masses,
is the gravitational constant,
and are the masses of the two objects,
is the distance between their centers.
3. Newton's General Binomial Theorem (Binomial Expansion):
For any real number and :
(1 + x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \cdots
4. Newton's Forward Difference Formula (Interpolation):
If is a function with values at equally spaced points, the forward difference formula for approximation is:
f(x_0 + h) \approx f(x_0) + \Delta f(x_0) + \frac{\Delta^2 f(x_0)}{2!} + \cdots
5. Newton's Method (Root-Finding Algorithm):
Newton's method is used to approximate the roots of a function. The formula is:
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
is the current guess,
is the function evaluated at ,
is the derivative of the function at .
6. Newton-Cotes Formula (Numerical Integration):
This family of formulas provides a way to approximate the integral of a function. One common example is the trapezoidal rule, which is a simple case of the Newton-Cotes method:
\int_a^b f(x) \, dx \approx \frac{b - a}{2} (f(a) + f(b))
These are some of the most important formulas linked to Newton's contributions to science and mathematics. Let me know if you'd like a deeper explanation of any specific formula.
ChatGPT?
@@SkibidiGyatSigmaToiletGamingcorrect
You used normy AI and call it "Asian"
@CypherInfintie it's
ChatGPT
@@nicco6818 lol
I just realized how animation vs math was created
Türkiye eğitim sistemi; 💀
The Romanian math is more complicated I am an student and I can confirm it😢
Confirm it then, crybaby
Fix your grammar
@CypherInfintie Bro what are you talking about? I write better than your mother 🤣
I school in Asia when I'm like 15 is hard but now Im in Harvard in the age of 19 it's easy
Highly doubt you were Even at harvard
Due to that spelling.
@@Fapolouslukasu realise english probably isnt his first language?
/w oldwokefan1
This requirement is presentated in the Harvard Website its selves
English Proficiency Requirement
Applicants who are non-native English speakers can demonstrate English proficiency in one of three ways:
Receiving an undergraduate degree from an academic institution where English is the primary language of instruction.
Earning a minimum score of 80 on the internet based test (iBT) of the Test of English as a Foreign Language (TOEFL)*
Earning a minimum score of 6.5 on the International English Language Testing System (IELTS) Academic test.*
Harvard strongly recommends Over 4 years of english with a strong writing component
@@Fapolouslukas 1: why do u capitalise random words?
2: maybe he just doesnt gaf about how he types on the internet
@Oldwokenfan1
That was completly unnecesary input.
I pasted those exactly from it's source
Being the Harvard websites its selves.
Alright Maybe he does'nt gave shit About it.
Ok guys, imma turn into a teacher rq..
PEMDAS. (4 operations)
10×(10÷2)+20-3
How do you solve it?
P - Parenthesis
E - Exponent (mostly not in solving)
M - Multiplication
D - Division
A - Addition
S - Subtract
To solve 10×(10÷2)+20-3, the parenthesis/numbers in the brackets should be solved first.
10 divided by 2 is equal to 5.
So, 10 divided by 5 is equal to 2.
Theres no exponent, so lets move on to adding.
2 plus 20 is equal to 22.
Onto subracting, 22-3 is equal to 19.
Therefore, the final answer is "19".
Sol:
10×(10÷2)+20-3
=2+20-3
=22-3
="19"
Tbh in my classroom they say its easy
Imagine paper of ISI Maths India ☠️☠️
Your university professors can’t solve every question of this paper and the paper is given by 16-17yr old students ☠️☠️
Just search paper of ISI Maths Chennai India =☠️
WHY DID YOU REDEEM IT
Bro do you know about ioqm, rmo, inmo?
@ I’m IOQM qualified ☠️
you think that’s American math? Well I goddamn wish the same thing
All continents is the same wdym?? 😂
Please tell me its a joke
@@SystemizandoThis comment is no joke. But the video is
I swear that American mathematics is the easiest treatment we have in the history of Iraqi mathematics😍💔
Meanwhile Arab (creators of mathematics) maths:💀💀☠️☠️
Its not arab?
@UnRaged we know..?
@@im_tiredd0.0 ?
who the hell said creators of maths were arabs mainly it devloped in china,india,greek and egypt and also calclus was devloped by newton one of the most important devlopment were done by these civilisation not arabs
@@Rudra-Raut811bhai algebra was created by arabs
I'm Asian student ( Vietnamese ). Our math not difficult because I'm 6 grade student
The squiggly line gave me chills 🥶❄️
Well well That USA math Is H.W of Our 6th grade students 😒😮💨
Song name?
Edit: How did the subject change from the song name to fucking bad habits💀
Life Letters never get used to people
@RareUnknown9978 ty
Sus@RareUnknown9978
I wish I knew
@@oofussasius i wish i knew who i wanna be
It is not Asian or American... It is math which is universal. Debate is over.
As an asian student i AGREE
its not true for only aisians
It's nothing to do with Asia.
well it actually has nothing to do with Asia I’m European and its probably almost the same anywhere else too
It has nothing do with Asia
@asterpawze I have friends in Europe and in Russia we studied in 5th grade what Europeans study in 7th grade
Memory reboot sounding lil bit different today
We got mr bean teaching maths before gta 6
The fact the he showed American math mathematicians is crazy
As an asian am a doctor ........ im 16 years old
child abuse
feeding the stereotypes ahh 🙏
Anime profile picture? Statement denied
I feel psycho after hearing this music with maths...
It's fcking true . My teacher just spamming us with π
As a proud Vietnamese person (Asian), this is true af.
Fun fact: this guy isn't even american
He's brazillian
Yes, he is, America is a continent, Brazil is on South America
@@SystemizandoThen he’s South American. America is not a continent. American is a nationality.
Он Американец, у вас даже с географией все плохо?🤡
@@Гидроэлектростанция-ж7о No, he is south american, you're so bad that can't even talk english with us
Primary school: 😄
Middle school: 😄
Grade 7-9: 😄
Grade 10+:
blud we got that math+++ hard lvl edition
That (x+ab²/b²)×(x⁸+x⁹) things💀
As an Asian student, there’s no saving us 😭
Asian math is so difficult but also powerful, the one who can understand it perfectly can find anything. Asian maths can solve so many things
As a HALF-Asian, I can confirm I knew how to do the Pythagoras Theorem and the Fibonacci Method at grade 5.
That’s normal……
thats normal bruv i now all areas all volumes fibonacci. arithmethic equation and the uh (sorry i dont understand this in english) but like the Un and Sn method then the ratio Un and Sn method. Combinatorics then cryptharithm then phytagoras then fibonacci. Lcm and that one other. And many more
Nice
Now do Lim
So wht the quest of fibomaci
@@kawasaki-id7ss fibonacci is a pattern of a number + 2 number before. for an example. 1.1.2.3.5.8.13.21 and so on.
Im almost dead by that math💀
actually, its the same, its just the order they learn each things
U forgot about african maths..It hard like asian here😂
So every asian has to do an edit on math and all americans look like mr bean if I’ m correct.
Math gonna kill us next quarter😭
Turkish Math's 1% : Asian maths
they really done teaching us next level shiz in middle school
LIFE LETTERS BE HITTING DIFFERENT🗣️🗣️🗣️🔥🔥🔥
turkish students:😃(🤬🤬🤬🤬🤬🤬🤬)
Look who's mad 😂
Grades 1-6:
7-11 grade:
I have it in Russia...
The man on the upper vídeo IS NOT AMERICAN, he is Brazilian, his RUclips channel name is "Professor Mr.Bean"
Since his appearance is a lot like Mr. Bean's he chose this name.
His classes are very cool btw🙃
POV:when u new to middle school
Math exams:
Are you like 12 year old?
@ uh… maybe…
It's like You need these when your stuck in a frickin cave with just A flashlight and a whiteboard and a marker
as an asian, we cry ourselves to sleep whenever we hear the mention of the word “mathematics”
They do the same stuff in America lol
Let’s write a list from 1-2000:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000