Never knew the Babylonians had a way to solve quadratics by completing the square 3000 years before the Arabs! This is such amazing stuff! I had to think a little bit before I understood their way of computing, although I'm very familiar with completing the square.
A possible mistake here at 15:10. The 30 by 30 square is 0.15, while the shaded area is 0.45. Therefore, the sum of the two is 1 and the big square is NOT 1 BUT 1 + the unknown.
I fell for that also but what I found is that "my square" is the unknown area (it's not 45), 45 is obtained by extending a side of "my square" to get a rectangle of length 1 and width sqrt(my square), so now I have " my square + 1*sqrt(my square) = 45).
W0w, I really did nail this shit. They say science changes from funeral to funeral. Who do I need to help? Add the first 1 from the repeated 1s in the prime sequence, e (1D gauge), sq 2 (2D gauge) and Pi (3D gauge) to the third decimal and you get 6.132. They had a two-triangle>pyramid>dynamic dome (6-point) x base 10 system of NUMBERS, the geometry is kinda primary. 1D factorial embedding up to a dynamic dipole in 3X2D on one side. I hit your Euclid vid already.
....wait...so, the formula the Babylonians use for a circle: *Area = C^2 ÷ 12* Means that they were using the luminaries to determine their calculations... Therefore *360° Circuit of the Luminaries = 360° of a Circle or Square* This would mean that a *1 Base Year = 360 Days* of *12 Months* which would mean that *1 Day = 36 Moments* of *12 Hours.* *Area = C^2 ÷ 12* *Area = 60°^2 ÷ 12* *Area = 360° ÷ 12* *Area = 30°* *Area = C^2 ÷ 12* *Area = 6^2 ÷ 12* *Area = 36 ÷ 12* *Area = 3*
In fact in book 2 you will find a variety of applications of this articular construction. . The reference to the square root is indicative of the standard unit: it is a square and it's sides are defined as I unit.of length. Multiplication is in fact duplication many times , so the construction may be split into sub units or enlarged into more manageable units.
It appears that the Egyptians and Babylonians taught by example. The quantities used were exemplary of the general procedure for the solution of a certain type of problem. So their quantities were like our variables.
If I'm interpreting what you've said correctly then I agree! I'm currently going through Book II of The Elements and the problem I run into is seeing that there should be real examples to utilize these concepts with, but the book is approached from a purely instructional POV.
Just found your channel. No idea what to think at this point. I agree we should take a more critical approach to maths education. Very interesting videos, thanks.
Puzzling over it I feel book2 proposition8 may bear directly on this procedure bearing in mind that we are asked to add 15 to 45 and those 15 are presumably drawn from the 30 by 30 duplication. , leaving a unit square short by 3 15 unit squares. , a gnomon of 3 i15 unit squares, that is to be clear squares of side units 15 . The master unit is a 60 by 60 square.
All world is interested in teaching and learning the Mesopotamian civilizations while we the people of these civilizations never taught anything but simple things!!!
I don't think its so much the "how" but "when". If civilization is older than we think, that means they figured this out a lot earlier than we think. That would be interesting, because it could demonstrate to us two things: 1) We've lost a lot of knowledge for various reasons. 2) Its possible that the technologies they were implementing could have been better than we think. (not talking aliens either).
Book2 proposition 6 of the Stoikeia explains the Hoyrup reference in detail .i must say it is clearer than your explanation! Book 2 is about the rectangular parallelogram and the Gnomon ( the L shaped figure). You can see that it is a more general treatment than this particular example.
I'm on Book 2 right now and and this concept felt very familiar. Tbh I to appreciate their explanation of this concept because Euclids book doesn't quite explain it the same way. Can you help explain it a little clearer? and is there any websites out there that go into details of these Props?
ThePhilosopher I am not sure what is available at the moment because unfortunately I am blind and my interests are focused elsewhere. If you google stoikeia you might get access to the Greek text. On RUclips I think there is an Indian professor dealing with the Euclidean propositions, but these propositions were meant to be studied and reflected on by actually drawing them. The basic line, usually a rectilinear line is divided arbitrarily. Using that division one is able to draw circle with either of the two parts as a radius. Using that circle one can construct any number of parallelograms. These parallelograms are not areas, they are the basic form . However you could make is it an absolute requirement (aitema) That you can construct a right angle/orthogonal line. Then you can construct rectangles and squares and apply the methodical description of the process. The process is not dependent on angle and so applies equally to rectangles and parallelograms. You do not need to know an area you just need to be able to identify identical forms and count the number of identical forms. This of course becomes equivalent to the modern concept of an area which as you can understand is the counting of a number of identical forms which are used as a standard.Because algebra uses the same method but use symbols instead of forms, These methods were locked away from the modern mind. Once you realise that the symbol is really a form, whether it is a line or a shape then you can understand why some of the translations are laughable. U Clh it deals with the basic parallelogram and then adding lines/producing or extending one of the sides in order to create the side for a larger form in which he then identified that gnomon. The propositions then explain relationships between the figures/forms within the construction, often in terms of lpgoi which simply translated means ratios or statements about the count of one form compared with another form using the same, commensurable measure/Monas. Such a Monas as you will see can be a line, the two-dimensional form, or a three-dimensional form. There is no need to quantify the Monas because it is the fundamental unit of quantities. The only requirement is that everyone agrees to a certain set of requirements set out at the beginning of the book as the requirements to study the book. These are often falsely called axioms, and the Greek clearly states these are the requirements! Axioms in fact are a much later concept outside of Euclid Stoikeis and may appear in so his later works all the work of the following geometer Who in fact redacted you could course to introduce the importance of the circle. Do not be fooled by Aristotelian logic, Aristotle never qualified as a mathematicos♥️
@@jehovajah I already have a PDF version that is English that translates from the Greek text on the other half of the page. Sorry for your ailment, but thank you for your feedback. I guess I'll keep researching to find deeper explanations.
ThePhilosopher Excellent. All you need now is inside from Yehovah into the Oriental mindset. The 19th century textbooks on geometry actually rewrite The Stoikeia according to modern French mathematical thought, which includes quite a lot of Aristotelian logic, counted to the Pythagorean school of thought. You will not find a deeper or more thorough treatment and in the works of Herman Grassmann especially in his 1844 work Die Ausdehnungs Lehre especially if you can read it in the German Yehovah rent to inside in your studies ♥️
That's an interesting point. @13:41 (note two points) the text says "Multiply 30 and 30. Add 15 to 45 = 1" The numbers to the right show 0.45 + 0.15 = 1 which I read as already being in Babylonian. But how did they write it? Modern notation sometimes puts a semi colon after the unit and commas after each place fraction i.e. [0;45]+[0;15] but as we are learning with the half which can be written as a 30 there is no zero. Its like looking at a clock and seeing 45 mins & 15 mins or in fractions 3/4, 1/4 and a 1/2.
Note: A " finger " ( AKA " horn " or qarnu in Akkadian ) was a measure of arcminutes used to determine eclipse magnitudes ( and others ) and represented 1/12 of the Sun or Moon diameter, approximate ) This is " qeren " in Hebrew, or " teba " in Egyptian The royal cubit was based on the astronomy convention of the " finger ", not vice versa 1 finger = 1 degree These ancient conventions are still used by modern astronomers www.fortworthastro.com/images/hand-degrees.gif You might want to examine why Egyptian astronomer-priests passed along knowledge of mathematical astronomy by usual strictly oral means
They used geometry and dimensions to calculate. Probably figured out our E8 theory of everything and had multidimensional thinking. Most of the “Temples” are actually depictions of math they found interesting. So in their design are formulas that were so mind blowingly interesting to them, they had to build the geometry of it in the 3d world they were living in. The pyramids are also NOT tombs and were build 12000years ago. They are actually power stations of some sort much like Nikola Tesla’s famous tower. We should show them more respect!
Whilst it is amazing to think that the creator of BM13901 and al Khwarizmi both inhabited the same geographically region one has to ask did "the method" travel further afield (say to India) before it returned some 3,000 years later?
But then why does the world keep accepting to call the theorem pythagoraen when we know for a facts Egyptians used those methodes 3000 years(proven by Pr Cheikh Anta Diop) before his birth ?
very interesting topic, thank you for that.
Loving this series so far. Thank you Daniel Mansfield for joining NJ Wildberger to present this topic. It's fascinating! :-)
keep making vids!!! thank u guys for your great work!!
Awesome guys!! Ancient mathematics is just so cool.
Never knew the Babylonians had a way to solve quadratics by completing the square 3000 years before the Arabs! This is such amazing stuff!
I had to think a little bit before I understood their way of computing, although I'm very familiar with completing the square.
A possible mistake here at 15:10. The 30 by 30 square is 0.15, while the shaded area is 0.45. Therefore, the sum of the two is 1 and the big square is NOT 1 BUT 1 + the unknown.
I fell for that also but what I found is that "my square" is the unknown area (it's not 45), 45 is obtained by extending a side of "my square" to get a rectangle of length 1 and width sqrt(my square), so now I have " my square + 1*sqrt(my square) = 45).
W0w, I really did nail this shit. They say science changes from funeral to funeral. Who do I need to help? Add the first 1 from the repeated 1s in the prime sequence, e (1D gauge), sq 2 (2D gauge) and Pi (3D gauge) to the third decimal and you get 6.132. They had a two-triangle>pyramid>dynamic dome (6-point) x base 10 system of NUMBERS, the geometry is kinda primary. 1D factorial embedding up to a dynamic dipole in 3X2D on one side. I hit your Euclid vid already.
....wait...so, the formula the Babylonians use for a circle:
*Area = C^2 ÷ 12*
Means that they were using the luminaries to determine their calculations...
Therefore
*360° Circuit of the Luminaries = 360° of a Circle or Square*
This would mean that a *1 Base Year = 360 Days* of *12 Months* which would mean that *1 Day = 36 Moments* of *12 Hours.*
*Area = C^2 ÷ 12*
*Area = 60°^2 ÷ 12*
*Area = 360° ÷ 12*
*Area = 30°*
*Area = C^2 ÷ 12*
*Area = 6^2 ÷ 12*
*Area = 36 ÷ 12*
*Area = 3*
In fact in book 2 you will find a variety of applications of this articular construction. . The reference to the square root is indicative of the standard unit: it is a square and it's sides are defined as I unit.of length. Multiplication is in fact duplication many times , so the construction may be split into sub units or enlarged into more manageable units.
It appears that the Egyptians and Babylonians taught by example. The quantities used were exemplary of the general procedure for the solution of a certain type of problem. So their quantities were like our variables.
If I'm interpreting what you've said correctly then I agree! I'm currently going through Book II of The Elements and the problem I run into is seeing that there should be real examples to utilize these concepts with, but the book is approached from a purely instructional POV.
I can't help being a little sad they didn't write 2C^2/25, which if I'm not mistaken, would've been incredible precise for the time.
Good video
Thank you very much for this video. Really makes me joyed as an Egyptian, even though unfortunately the math curriculum in Egypt lags.
أنا مصري برضو, ممكن أتواصل معاك لو تعرف تفيدني بأي شيء؟ (كنت عايز أقدم محتوى قريب لده).
Just found your channel. No idea what to think at this point. I agree we should take a more critical approach to maths education. Very interesting videos, thanks.
Curiouser and curiouser, there is more than one way to reckon with figures
Puzzling over it I feel book2 proposition8 may bear directly on this procedure bearing in mind that we are asked to add 15 to 45 and those 15 are presumably drawn from the 30 by 30 duplication. , leaving a unit square short by 3 15 unit squares. , a gnomon of 3 i15 unit squares, that is to be clear squares of side units 15 . The master unit is a 60 by 60 square.
Thanks Sir making videos
Heard the news piece on ABC 702 :) nice!!!
All world is interested in teaching and learning the Mesopotamian civilizations while we the people of these civilizations never taught anything but simple things!!!
Looks like mesopotamian were far ahead of egyptians in math. But where and how did they get this knowledge of math? Its so advanced.
I don't think its so much the "how" but "when". If civilization is older than we think, that means they figured this out a lot earlier than we think. That would be interesting, because it could demonstrate to us two things: 1) We've lost a lot of knowledge for various reasons. 2) Its possible that the technologies they were implementing could have been better than we think. (not talking aliens either).
@@thephilosopher7173 I agree. Also, what I question is that "Did that knowledge pass down to us?" and if "No." then "Why? What happened?".
Book2 proposition 6 of the Stoikeia explains the Hoyrup reference in detail .i must say it is clearer than your explanation! Book 2 is about the rectangular parallelogram and the Gnomon ( the L shaped figure). You can see that it is a more general treatment than this particular example.
I'm on Book 2 right now and and this concept felt very familiar. Tbh I to appreciate their explanation of this concept because Euclids book doesn't quite explain it the same way. Can you help explain it a little clearer? and is there any websites out there that go into details of these Props?
ThePhilosopher I am not sure what is available at the moment because unfortunately I am blind and my interests are focused elsewhere. If you google stoikeia you might get access to the Greek text. On RUclips I think there is an Indian professor dealing with the Euclidean propositions, but these propositions were meant to be studied and reflected on by actually drawing them. The basic line, usually a rectilinear line is divided arbitrarily. Using that division one is able to draw circle with either of the two parts as a radius. Using that circle one can construct any number of parallelograms. These parallelograms are not areas, they are the basic form . However you could make is it an absolute requirement (aitema) That you can construct a right angle/orthogonal line. Then you can construct rectangles and squares and apply the methodical description of the process. The process is not dependent on angle and so applies equally to rectangles and parallelograms. You do not need to know an area you just need to be able to identify identical forms and count the number of identical forms. This of course becomes equivalent to the modern concept of an area which as you can understand is the counting of a number of identical forms which are used as a standard.Because algebra uses the same method but use symbols instead of forms, These methods were locked away from the modern mind. Once you realise that the symbol is really a form, whether it is a line or a shape then you can understand why some of the translations are laughable. U Clh it deals with the basic parallelogram and then adding lines/producing or extending one of the sides in order to create the side for a larger form in which he then identified that gnomon. The propositions then explain relationships between the figures/forms within the construction, often in terms of lpgoi which simply translated means ratios or statements about the count of one form compared with another form using the same, commensurable measure/Monas. Such a Monas as you will see can be a line, the two-dimensional form, or a three-dimensional form. There is no need to quantify the Monas because it is the fundamental unit of quantities. The only requirement is that everyone agrees to a certain set of requirements set out at the beginning of the book as the requirements to study the book. These are often falsely called axioms, and the Greek clearly states these are the requirements! Axioms in fact are a much later concept outside of Euclid Stoikeis and may appear in so his later works all the work of the following geometer Who in fact redacted you could course to introduce the importance of the circle. Do not be fooled by Aristotelian logic, Aristotle never qualified as a mathematicos♥️
@@jehovajah I already have a PDF version that is English that translates from the Greek text on the other half of the page. Sorry for your ailment, but thank you for your feedback. I guess I'll keep researching to find deeper explanations.
ThePhilosopher Excellent. All you need now is inside from Yehovah into the Oriental mindset. The 19th century textbooks on geometry actually rewrite The Stoikeia according to modern French mathematical thought, which includes quite a lot of Aristotelian logic, counted to the Pythagorean school of thought. You will not find a deeper or more thorough treatment and in the works of Herman Grassmann especially in his 1844 work Die Ausdehnungs Lehre especially if you can read it in the German Yehovah rent to inside in your studies ♥️
How did the Babylonians represent the number 0.45, which you quote?
Charles A Berg
Charles A Berg
Sexagesimally. (27)/60?
That's an interesting point. @13:41 (note two points) the text says "Multiply 30 and 30. Add 15 to 45 = 1"
The numbers to the right show 0.45 + 0.15 = 1 which I read as already being in Babylonian. But how did they write it? Modern notation sometimes puts a semi colon after the unit and commas after each place fraction i.e. [0;45]+[0;15] but as we are learning with the half which can be written as a 30 there is no zero. Its like looking at a clock and seeing 45 mins & 15 mins or in fractions 3/4, 1/4 and a 1/2.
Note:
A " finger " ( AKA " horn " or qarnu in Akkadian ) was a measure of arcminutes used to determine eclipse magnitudes ( and others ) and represented 1/12 of the Sun or Moon diameter, approximate )
This is " qeren " in Hebrew, or " teba " in Egyptian
The royal cubit was based on the astronomy convention of the " finger ", not vice versa
1 finger = 1 degree
These ancient conventions are still used by modern astronomers
www.fortworthastro.com/images/hand-degrees.gif
You might want to examine why Egyptian astronomer-priests passed along knowledge of mathematical astronomy by usual strictly oral means
Babylonian maths from scratch 💜
They used geometry and dimensions to calculate. Probably figured out our E8 theory of everything and had multidimensional thinking. Most of the “Temples” are actually depictions of math they found interesting. So in their design are formulas that were so mind blowingly interesting to them, they had to build the geometry of it in the 3d world they were living in. The pyramids are also NOT tombs and were build 12000years ago. They are actually power stations of some sort much like Nikola Tesla’s famous tower. We should show them more respect!
Why are you not mentioning Otto Neugebauer who published this interpretation of Plimpton 322 in 1945?
Seqed ratios 22/28, or
22/7 Pi, 28/7 a square.
Whilst it is amazing to think that the creator of BM13901 and al Khwarizmi both inhabited the same geographically region one has to ask did "the method" travel further afield (say to India) before it returned some 3,000 years later?
The Pythagorean theorem is a natural theorem that without school, to that you would have found it anyway
That's how everything is but only a few select individuals can actually find it out ..dont act like the whole population of earth could
Quite right. Just don’t roll your mind over.
But then why does the world keep accepting to call the theorem pythagoraen when we know for a facts Egyptians used those methodes 3000 years(proven by Pr Cheikh Anta Diop) before his birth ?
That's the same for pascal's triangle and many other theorems.