Pentagons and the Golden Ratio - Numberphile

Watch on YouTube

Show annotations

Download is disabled.

154,126

7,365

77

Genre: Science & Technology

Family friendly? Yes

Wilson score: 0.9871

Rating: 4.9586 / 5

Engagement: 4.83%

Numberphile

Subscribe | 3.22M

Shared February 9, 2020

Continuing on from Zvezda's previous video about Ptolemey's Theorem (see: https://youtu.be/bJOuzqu3MUQ) now we use it to prove some cool stuff with pentagons and equilateral triangles.
More links & stuff in full description below ↓↓↓

Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos

Zvezda's webpage: https://math.berkeley.edu/~stankova/

Golden Ratio: https://youtu.be/sj8Sg8qnjOg

Epic Circles: https://youtu.be/sG_6nlMZ8f4

Triangle Magic Highway: https://youtu.be/wVH4MS6v23U

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outr...

And support from Math For America - https://www.mathforamerica.org/

NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub

Videos by Brady Haran

Patreon: http://www.patreon.com/numberphile

Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile

Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/

Brady's latest videos across all channels: http://www.bradyharanblog.com/

Sign up for (occasional) emails: http://eepurl.com/YdjL9


Numberphile

This continues from our proof of Ptolemy's Theorem --- https://youtu.be/bJOuzqu3MUQ

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

6alecapristrudel

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

warmCabin

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

2 weeks ago | [YT] | 96

TheFulcrum2000

"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

lchap

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