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1,468,619 Views • Mar 20, 2024 • Click to toggle off description
This is a short, animated visual proof finding the area bounded between three mutually tangent unit circles.

Have a different solution? Share it in the comments!

If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualProofs. Thanks!

Check out these related videos:
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This animation is based on an exercise from Roger Nelsen's and Claudi Alsina's wonderful book "Icons of Mathematics". You can find the book and other information about it at the links below

(I may receive commissions from this paid link) : Icons of Mathematics from Amazon amzn.to/3L5U44S

www.maa.org/press/maa-reviews/icons-of-mathematics…

bookstore.ams.org/dol-56/

#manim #math #mathvideo #mathshorts #geometry #hexagon #animation #theorem #pww #proofwithoutwords #visualproof #proof #area #root3 #pww​ #proofwithoutwords​#proof​ #algebra #areas #mathematics​ #mathvideo​ #mtbos

To learn more about animating with manim, check out:
manim.community/
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Views : 1,468,619
Genre: Education
License: Standard YouTube License
Uploaded At Mar 20, 2024 ^^


warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
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RYD date created : 2024-11-21T21:30:45.687249Z
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1,876 Comments

Top Comments of this video!! :3

@Zangoose_

8 months ago

When you colored in the pink, it was over. Good stuff here

8.9K |

@Shion-u8l

6 months ago

Solving this correctly was the confidence boost I need during my regular 3 am depressive episode.

712 |

@shanewright4650

7 months ago

Yes, this is exactly how I solved it myself. The general formula would be r^2(sqrt(3) - π/2)

85 |

@peternicks7049

4 months ago

Straight away. Always good to get a mathematical pick me up when feeling inadequate.

59 |

@GREGGRCO

7 months ago

I've been away 40 years from this !
I was on the right path !!
I didn't see the Equal lateral triangle in the middle! Paused the video and finished !!
That was great ! Thanks !! I was very interested in the comments ! Gonna look at those methods !

40 |

@NevazkKa

1 month ago

This is why i love geometry. I Never thought about calculating the area between 3 tagent circles, but the exact moment i saw this I knew in every step what the way to the answer would be. This is simply beautiful

3 |

@madtscientist8853

8 months ago

That is called a G-STRING

4K |

@Edenival.v0x

6 months ago

1. Triangle
2. Area of sector
3. Subtract area of triangle and area of sectors
4. Answer

42 |

@lexacutable

8 months ago

Hrm.

I think I do indeed need to investigate this curvy area more closely.

1.2K |

@Truly_Abhinav

6 months ago

Thank you sir, mera 2 hafte me exam hai aur mujhe pura samajh aagya, meine paheli bar aapki video dekhi hai aur ab mujhe pata chala hai aapko log best teacher kyu khete hai

2 |

@wermh3719

7 months ago

Integration has never failed me and this time was no exception 🗿

5.5K |

@Codesage-r1k

2 months ago

I love this kind of problems not too hard and not too easy.

10 |

@dhhfkkjb6891

7 months ago

Now i know how to calculate the area of a g-string thanks

988 |

@Bubble_Gum7505

5 months ago

At first we need to find area of triangle, then subtract area of circles from it.
For example Radius - 5 m
1) Area of triangle:
(10×10)/2= 50 m
2) Need to find the area of 3 pieces of circles. Area of one whole circle:
3,14×5²= 78,5 m
Angle of piece - 60° because sum of angles in triangle is always equal to 180°. Area of piece of one circle is: 78,5 m×(60°/360°)= 13,083 m. And area of three pieces is equal to 39,249 m. 50-39.249= 10,75; ~11 m

4 |

@sirsamiboi

8 months ago

This solution is so satisfying

426 |

@afrophoenix3111

6 months ago

I had the same methodology (and result), but your explanation and execution were far more elegant than mine.
Thanks for the chance to flex the geometry muscles.

1 |

@mennolente4807

7 months ago

I drew hexagons around circles, radius equals apothem, area hexagon minus area circles, divide by three to get rid of the unnecessary bits.

423 |

@ZekeRaiden

1 week ago

I did mostly the same process, but simplified the circular areas first. Each arc is 1/6th of a circle, so three of them make a half-circle. The unit half-circle has area pi/2.

1 |

@goggypoggy

8 months ago

wow, I actually solved it the EXACT same way! I'm so proud of myself!!!

1.4K |

@coopernoble6139

6 months ago

I’m so proud of myself for figuring it out before. You can form an equilateral triangle, and then subtract three 60 degree sections of the circles. So 2r^2 - (pi*r^2)/6

1 |

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