Pentagons and the Golden Ratio - Numberphile

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Shared February 9, 2020

Continuing on from Zvezda's previous video about Ptolemey's Theorem (see: now we use it to prove some cool stuff with pentagons and equilateral triangles.
More links & stuff in full description below ↓↓↓

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This continues from our proof of Ptolemy's Theorem ---

2 weeks ago | [YT] | 107

Jeremias Figueiredo

any hard math problem
Prof. Zvezda: "I remember struggling to solve this problem at kinder garden"

2 weeks ago | [YT] | 133

Ethan Cheung

I laughed so hard when Brady reconfirmed that was not the factorial. He must have been so traumatised by numberphile

2 weeks ago | [YT] | 641


Theorem: every Bulgarian math teacher has this accent in any language they speak.

2 weeks ago | [YT] | 230

Edward Morales

Dude I cannot get over how brady took an almost quiet deep breath when he saw the golden ratio

2 weeks ago | [YT] | 291

The Rock'n'Roll Millennial

All Numberphile guests are wonderful, but Zvezda is my personal favorite. :)

2 weeks ago | [YT] | 44

Joaquin Vigara

“ oh look an homogeneous equation I can do miracles with that”
I’ve laughed so hard😂😂😂😂

2 weeks ago | [YT] | 18

Vital Spark

4:00 "could be the most famous ratio?" Zvezda, may I introduce you to the ratio of a circle's circumference divided by its diameter?

2 weeks ago | [YT] | 119


The way she draws b really makes you see how it evolved from B

2 weeks ago | [YT] | 96


"The Bermuda triangle?" lol :-)

2 weeks ago (edited) | [YT] | 168

Linda Ristevski

The sequel is even better than the first! Blown away.

2 weeks ago | [YT] | 99

David Thornley

It's one thing to see this elegance in the explanation, but how mind bending must it have been to originally conceive the inversion principle and apply it ? !

2 weeks ago | [YT] | 145


Everyone deserves a math teacher who is as passionate as Zvezda.

2 weeks ago | [YT] | 10

C. W. Tai

Somehow, "!" Is unintendedly one of the highlights.

2 weeks ago | [YT] | 22

Alex Potts

2:50 okay that's a pretty crummy regular pentagon. Get me Professor Eisenbud, a ruler and compass and a gratuitously complicated list of instructions...

2 weeks ago (edited) | [YT] | 75

steven wonder

What an ingenious proof, the stark elegance of it all is just mind blowing

2 weeks ago | [YT] | 50

Tibor Grün

The way I remember the golden ratio is: taking 5 and 1/2 and applying the operations in descending order: 5 ^(1/2) *(1/2) +(1/2)

2 weeks ago | [YT] | 59

Essentials Of Math

And one can use the Pentagon relationship to show that cos(36 degrees) = golden ratio /2, and cos(72 degrees) = (golden ratio - 1)/2

2 weeks ago | [YT] | 43

Alexander Roderick

This is insane! We have to inform the Pentagon!

Oh wait, they already know.

2 weeks ago | [YT] | 30

James Conant

She's a gifted teacher.

2 weeks ago | [YT] | 4