A fun probability puzzle with a neat geometric solution.

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Programs used:

► Cinema 4D

► Processing

Music by

[MuPrimeMath]

Your geometric proof animations are so colorful and clean at the same time! Everything flows so nicely. I love it!

[johandaun]

I didnt think twice when I saw your video getting notified

[amir]

High quality content, visually and audibly pleasing. Thank you!

[jamesmnguyen]

I didn't try to prove the solution but somehow my brain guessed the solution space of this problem is probably a semicircle.

[SnydeX]

I was able to intuit the solution and am feeling pretty smart right now, even though I probably shouldn't.

[jkid]

I paused when instructed and came up with pi/8. This was a surprisingly straightforward application of Thales theorem for a YouTube math puzzle :)

[yeast]

I could watch these videos forever. Combining interesting mathematics with great visuals and audio is about as good as it gets

[ollolol]

Here comes a challenging question:
How about the possibility of α > x° for any given x?

[cloudwolf]

Dude, I literally mentioned and recommended this channel to a friend today and we get a new video? Nice timing.

[vukasinkrsmanovic]

Video quality is on the whole another level and also explanations. I really love and apreciate the fact that you first prove theorems in explanings and than use it. Keep it up, you are amazing!

[cardiomatica]

I don't know how someone can do such amazing videos. Please keep the great work. ThinkTwice, 3Blue1Brown and others math channels are not just incredible in content but also ethereal in design and animation.

[Aleksandar]

Not only are you awesome at animating but you give your channel a dope vibe with the music. Who said math couldn't be relaxing?

[imelse]

The longest video on your channel! And it's so much easier to understand everything and feel the beauty of math this way! Absolutely amazing. Mldc

[i-teach-math]

I like your method of not having any voice overs. It is just the visuals and the math. Good job!

[SaNjA]

me: it's gotta be about 39%


Think Twice, an intellectual: π / 8


me: *surprised pikachu face*

[damianmatma]

Additional question:
What is the probability that |<APB| = 90 degrees?

Since the width of the semicircle arc in 04:27 is zero, so the area of the semicircle arc is zero, so this probability equals:
P( |<APB| = 90 degrees ) = Area of the semicircle arc / Area of the square = 0 / 1 = 0.

But, logically thinking, this probability should be greater than zero and maybe the way, in which I try to calculate it, is wrong.

Please, help me.

[aaronr.]

Pretty awesome but at 5:20 I would suggest that the purple region represents alpha <= 90. Otherwise, it gives the impression that you can subtract the area of the semi-circle from the area of the square in order to find the probability of alpha < 90. But I guess a simple subtraction here would not work because you would have to discount for the very thin band where P falls smack dab along the circumference resulting in alpha == 90.

[alexandersanchez]

Thanks for the reminder to pause and figure out the problem beforehand. I was so mesmerized that I would have just watched without the thought even occurring to me!

[ferrucciocastellini]

I have a harder question: what is the average angle that you get

[perova]

I'been suscribed to your channel for a while, and I gotta say i really love your videos. They're really well made and beatifully animated, plus i love that your proofs focus on de visual and geomtric side of theorems. Keep up the good work! Love from Argentina.