The Helicone Numberscope: Mathematical Superpowers Hidden in a Simple Toy

2025-01-06

[public] 20.0K views, 1.82K likes, dislikes audio only

This is a corrected version of a video that I uploaded two days ago. After a critical mistake was discovered in the "Nature's Numbers" part of the video, I decided to scrap the original video, fix the errors and republish the video (many more hours down the drain :( Anyway, had to be done. Just in case you are wondering my list of best approximations of pi did not fit in with my definition. This was first pointed out by @typha

I've collected the comments on the original video in this pdf file

https://www.qedcat.com/phyl/comments_collection.pdf

If you've got access to Mathematica, you can download my Helicone lab here: https://www.qedcat.com/phyl/helicone.nb

0:00 Intro

2:48 Helicone lab!

9:41 Fibonacci Christmas tree

12:28 Number scope

17:22 Nuts and bolts

23:41 Fractional angles

27:34 3, 22/7, ...

34:07 Nature’s numbers

41:45 Best Fibonacci fractions

43:36 Original Helicone Puzzle

45:55 Microscope zooming spectacle

47:05 Thanks!!

John Edmarks website with sections dedicated to his helicone and presentations by him about his work:

https://www.johnedmark.com/

http://www.johnedmark.com/#/rotating/

http://www.johnedmark.com/talks

If you want to buy one of these helicones google both "helicone" and "lollipopter".

The earlier Mathologer videos about the golden ratio and the Fibonacci numbers in nature referred to in this video:

The fabulous Fibonacci flower formula /youtube/video/_GkxCIW46to

Infinite fractions and the most irrational number /youtube/video/CaasbfdJdJg

Here is a bare bones version of the microscope: https://demonstrations.wolfram.com/PhyllotaxisExplained/

The technical term for Wolfram's spikey is Rhombic Hexecontahedron.

There is also a plant called Heliconia. However it looks nothing like the Helicone :)

Idea for the real-life Fibonacci Christmas tree: individually addressable LEDs. See, for example, this intro https://www.youtube.com/watch?v=LOimwthcdqo&feature=youtu.be

Mathologer junior is my son Karl and the Mathologer "junioress" behind the camera is my daughter Lara. Thanks Lara and Karl! And in this video we are paying a visit to my office at Monash University in Melbourne, Australia.

22/7 was found by Archimedes in the second century as part of the strict inequality 223/71 less than pi less than 22/7 and 377/120 was mentioned by Ptolemy in the 3rd century.

In Chinese mathematics, the fractions 22/7 and 355/113 are known as yuēlǜ (约率; 'approximate ratio') and mìlǜ (密率; 'close ratio').

Music: Christmas tree by Zac Nelson, Tea time by Ty Simon and I promise by Ian Post,

T-shirt: Pretty sure it's this one https://www.etsy.com/listing/720022200/pi-christmas-math-science-algebra-gift

Enjoy!

Burkard