I'm a physics professor. I love your videos. The "3 2 1" and the beginning and "how exciting" at the end are a great "gimmick." Your voice, delivery and graphics are perfect. Thanks for the entertainment.
You'll like this puzzle. You have a friend who lives exactly 250km away, and your elevations are identical. You have set up poles in your backyards which are at a height of precisely 4.33m. One day when it is sunny at both of your houses, your friend calls you. “The sun is exactly overhead. My pole casts no shadow.” You check your pole, and you see its shadow measures 17cm. What is the circumference of the Earth? (Assume the poles are perfectly vertical, of course, in that their bases point exactly to the center of the planet.)
I got 39,998,823.45 meters. The earths actually circumference is 40,075,017 meters. That’s 99% close! Thanks for the problem man. I’m really proud I managed to do that
@@elgringo4923 It is a fun one, and the shadow measurement would have to be to a few decimal places of millimeters to be accurate enough. I think your result is well within tolerances ;)
@@ampleman602 The angle between the sun's rays is actually negligible. A ray of light from one side of the sun and one from the opposite side will vary by about half a degree, depending on where we are in orbit. It's so close to parallel at this range.
Nice one, I like that you used a proportion to solve it. My solution reasoned that both triangles are 30-60-90 triangles because of the smaller triangle having a short leg of r and a hypotenuse of 2r. Then I solved R=3r (because the big triangle hypotenuse must be 2R) and solved the area using pi*r^2.
@@BonIsHappyXD He used proportion since he is then able to relate the known quantities of the small triangle to the big ones. Proportion simply means that a scale factor, s, is the difference between the two.
@@BonIsHappyXD Maybe this helps: Both triangles have the same angle (lets call it alpha) on the left side. Both triangles are right triangles. So: for the little triangle the sin(alpha) is defined as r/2r and for the big one sin(alpha) = R/(R+3r). Since the angle alpha is constant across both triangles both expression are equal. --> r/2r = R/(R+3r)
Love your videos Andy. It's always good to take a step back and relearn earlier and less complicated math that I have kind of forgotten over the years. I have to say, you are making this engineer re-love Math again, and helping me rejuvenate my desire for engineering.
Just discovered this channel, watched a bunch of these videos, admittedly never bothering my ass to solve them myself. I just live for that ‘how exciting’ at the end
Alternatively, could you use the first box to find the value of little r (1 over the square root of pi), and then plug that into the equation when you have big R in terms of little r? Actually… now that I’ve typed it, Andy’s method is faster…
Small radii are 1/sqrt(pi) Distance between outer circle centre and big circle centre is (3/sqrt(pi) + R That can be the hypotenuse of a right triangle The corresponging hypotenuse between the small circle centres is 2/sqrt(pi) and the short side of the triangle is 1/sqrt(pi) (2/sqrt(pi)) divided by (1/(sqrt(pi)) is (2*sqrt(pi))/sqrt(pi) = 2, so this proves that the triangle is a 30,60,90 (the hypotenuse is twice the length of the shortest side). This allows calculation of the large circle's radius: (3/sqrt(pi)) + R = 2R, so the radius of the large circle is (3/sqrt(pi)) Square this for 9/pi (9pi)/pi = 9. Large circle area is 9 un^2 Your way was much cleaner, but hey, I got there :)
10 second answer: little circle is 1r far away from the first one, and its radius is 1r, big circle is 3r far away from the first one therefore R is 3r, because of the thales theorem, therefore surface area of the big circle is 1Pi * 3^2 = 9Pi
You forgot the pi!! You accidentally dropped the pi for the area of the circles. Pi times 1 is pi, not one. Similarly pi times 9 is nine pi, not nine. So the area of the blue circle is actually 9 pi
My solution involved realizing that the situation with the little circle and the big circle touching the lines is similar. The little circle is 1r away from the tip of the lines, while the big circle is 3r away. This means the scale factor is 3, and since 2d objects scale at a rate of s^2, I got 1 * 3^2 = 9
Wow, I felt so confident in my answer until I saw how one error I did messed my answer all up 🥲 When I set up the proportions I didn't cancel out the little r's, so when I was cross multiplying I ended up with: 2 x R x r = R x r + 4r // - R x r R x r = 4r // : r R = 4 Surface = 2piR = 2 x 4 x pi = 8 x pi units sq. And then I learned I was off. How disappointing 😆
Andy grew a beard in the time it took to solve this problem. I'd love to see the math on his budget for razors!
Holy shit! It grew incrementally throughout the video. How did he do that! Film 30 seconds a day for 5 days?
The clothes hat and hair never change???
Probably figured out answer, then filmed smaller sequences in reverse order, and trimmed/shaved when got closer to the "beginning" of the problem
concentrate on the math man geeze
He's just built different
I'm a physics professor. I love your videos. The "3 2 1" and the beginning and "how exciting" at the end are a great "gimmick." Your voice, delivery and graphics are perfect. Thanks for the entertainment.
You look like Guy Fieri
Long live Physics 🫡
1:40 He cross multiplied his beard
Several hours later...
I didn't even notice
Capital R❌
Uppercase R❌
BIG R✅
Little r✅
little R
@@tai0fps I forgot that one :(
Littler - the teenage darting sensation. How exciting!
Lit-ul r ✅
Hard R?
That's the most rapid beard growth I've ever seen! The math was good too.
Lit-UHL radius gang
He's just pronouncing the word correctly
It sounds like how Alan from Smiling Friends would say it
Dude. Thanks for making these videos. I've been enjoying them.
How exciting
the way Andy pronounces lid'tle is so endearing
Was half expecting a razor ad at the end. Or is this a set up for the next video...how fast does Andy's facial hair grow? 🧔🏻♂
Calculate the time and length it took the beard to show since starting the video
Yes, find the rate of change.
Wtf I didn't even notice that 😅
You'll like this puzzle. You have a friend who lives exactly 250km away, and your elevations are identical. You have set up poles in your backyards which are at a height of precisely 4.33m.
One day when it is sunny at both of your houses, your friend calls you. “The sun is exactly overhead. My pole casts no shadow.” You check your pole, and you see its shadow measures 17cm.
What is the circumference of the Earth? (Assume the poles are perfectly vertical, of course, in that their bases point exactly to the center of the planet.)
I got 39,998,823.45 meters. The earths actually circumference is 40,075,017 meters. That’s 99% close!
Thanks for the problem man. I’m really proud I managed to do that
Is that a right question? the distance from the sun would have to be known to make the equation
@@ampleman602 i made the assumption that the suns light shines perfectly in the same direction at all locations
@@elgringo4923 It is a fun one, and the shadow measurement would have to be to a few decimal places of millimeters to be accurate enough. I think your result is well within tolerances ;)
@@ampleman602 The angle between the sun's rays is actually negligible. A ray of light from one side of the sun and one from the opposite side will vary by about half a degree, depending on where we are in orbit. It's so close to parallel at this range.
Nice one, I like that you used a proportion to solve it. My solution reasoned that both triangles are 30-60-90 triangles because of the smaller triangle having a short leg of r and a hypotenuse of 2r. Then I solved R=3r (because the big triangle hypotenuse must be 2R) and solved the area using pi*r^2.
can u explain why he used proportion in that scenario, i dont quite get it 😓
@@BonIsHappyXD He used proportion since he is then able to relate the known quantities of the small triangle to the big ones. Proportion simply means that a scale factor, s, is the difference between the two.
@@BonIsHappyXD
Maybe this helps:
Both triangles have the same angle (lets call it alpha) on the left side. Both triangles are right triangles. So: for the little triangle the sin(alpha) is defined as r/2r and for the big one sin(alpha) = R/(R+3r). Since the angle alpha is constant across both triangles both expression are equal. --> r/2r = R/(R+3r)
Love your videos Andy. It's always good to take a step back and relearn earlier and less complicated math that I have kind of forgotten over the years. I have to say, you are making this engineer re-love Math again, and helping me rejuvenate my desire for engineering.
I always look forwards to the "How exciting" at the end :p
Always a delight to find a new video from you.
The reason why this was difficult for me...is because I made it too difficult. You set this up much simpler than I was expecting.
How Exciting.
Just discovered this channel, watched a bunch of these videos, admittedly never bothering my ass to solve them myself. I just live for that ‘how exciting’ at the end
+10 enunciation to say lit-tuhl R so you avoid sounding like youre saying "littler"
Wow! Your facial hair grows fast! Nice explanation, though...as always.
I actually wonder how you figure out the solutions to these questions cuz I’d never think of any of these solutions. Massive respect for this guy 👏🏻👏🏻
He probably recorded backwards, must been so much work
The beard is melting my brain
That beard though.....How exciting.
How exciting
Alternatively, could you use the first box to find the value of little r (1 over the square root of pi), and then plug that into the equation when you have big R in terms of little r? Actually… now that I’ve typed it, Andy’s method is faster…
Hiiii, love you're math vids, they teach me stuff🎉🎉
Small radii are 1/sqrt(pi)
Distance between outer circle centre and big circle centre is (3/sqrt(pi) + R
That can be the hypotenuse of a right triangle
The corresponging hypotenuse between the small circle centres is 2/sqrt(pi) and the short side of the triangle is 1/sqrt(pi)
(2/sqrt(pi)) divided by (1/(sqrt(pi)) is (2*sqrt(pi))/sqrt(pi) = 2, so this proves that the triangle is a 30,60,90 (the hypotenuse is twice the length of the shortest side).
This allows calculation of the large circle's radius:
(3/sqrt(pi)) + R = 2R, so the radius of the large circle is (3/sqrt(pi))
Square this for 9/pi
(9pi)/pi = 9.
Large circle area is 9 un^2
Your way was much cleaner, but hey, I got there :)
Woah! That question was literally fun 🔥
10 second answer:
little circle is 1r far away from the first one, and its radius is 1r,
big circle is 3r far away from the first one therefore R is 3r, because of the thales theorem,
therefore surface area of the big circle is 1Pi * 3^2 = 9Pi
Yup, that's how I did it too, except that I only intuited Thales theorem. Also, it's 9 not 9pi, because the little circles have area 1.
My day is exciting bc of this
Excellent, I played the math with my son (7th grade), and he find it interresting. 👍
This was fun while it lasted thank you
A hairy problem. Facial hairy.
You forgot the pi!! You accidentally dropped the pi for the area of the circles. Pi times 1 is pi, not one. Similarly pi times 9 is nine pi, not nine. So the area of the blue circle is actually 9 pi
My solution involved realizing that the situation with the little circle and the big circle touching the lines is similar. The little circle is 1r away from the tip of the lines, while the big circle is 3r away. This means the scale factor is 3, and since 2d objects scale at a rate of s^2, I got 1 * 3^2 = 9
After 1 radius, a circle of 1^2 appears.
After 3 radii, a circle of 3^2 appears.
You could have used deltoid geometry for this question and found the solution in 30 seconds.
What software do you use? Can you make a tutorial?
if anyone wants to know, the small circles have a radius of 1/sqrt(π) the large circle has a radius of 3/sqrt(π)
Very exciting!
Simply by looking at the drawing I assumed R = 3r which turned out to be correct. Is my assumption valid or is it just a coincidence?
Hello, Andy👋
How exciting!
Yay Double Box appears!!!
The beard is sexy.
Exciting :)
how did you formulate
that
1r/2r = R/R +3r
i just wanna know since i dont knoe the theory behind this
How long does it take him to actually solve it cause some of these soo difficult, or does he already have the answer
Wow, I felt so confident in my answer until I saw how one error I did messed my answer all up 🥲
When I set up the proportions I didn't cancel out the little r's, so when I was cross multiplying I ended up with:
2 x R x r = R x r + 4r // - R x r
R x r = 4r // : r
R = 4
Surface = 2piR
= 2 x 4 x pi
= 8 x pi units sq.
And then I learned I was off.
How disappointing 😆
Now i will chalenge you to discover the radius of the little circule
that was satisfying
Bro did the solution in reverse lol 😂
👏👏
very exciting indeed
Nice
Ayyy I finally figured one out before watching the video, and used the same method (basically)
How did your beard grow during the video?
Why the centres on the same straight line
do we need the units if the original question doesn't have it?
I love liTTle r.
Counter for "liddle" vs "little"
liddle = 3
little = 22
may i know what software you use as the whiteboard in the video?
He did a video on how he animates this, check his channel.
Bro thinks he's Thales 🏆
are you sir a school teacher or academics or you just like math?
I got this one
Please shame to be so exciting 🙂
My dumbass read it as “radius of 1” and was lost tryna figure out how I got 9pi for a minute
This is how pirates sound when doing maths.
Nice beard
I wish my mustache grew that fast 😜😂😜
Kids stuff but better than brainrot
I just learned the I pronounce "little" wrong. How exciting.
20 years calculating this one... Look at the beard
How existing
LiTTle r
Hii
Hyhy
First
How exciting. Now shave. 🧔♂️🪒👨