Explaining Shapes Of Constant Width

In this video I'll share with you some of the things that interested me about shapes of constant width. Information about some of the stuff shown here was pretty tough to find online, like the visual representation of the Minkowski sum and the construction of the Meissner tetrahedron.
For more information, 3d models and the templates I used:
www.rad-head.com
I also made a build video where I show the process of making this set of shapes:
• Making Shapes of Const...
If you like what I do and want to support rad-head:
/ radhead
A great book on the subject (affiliate link):
amzn.to/2pT72JK
Similar products from some pretty cool guys:
mathsgear.co.u...
mathsgear.co.u...
Music: www.bensound.com

[@carolinedumogho3417]

Amazing! I've never seen anything like this. In all my boring years of school, geometry has never been more interesting!

[@radhead]

Thanks :)

[@torblikra9155]

Loved the explination. I realy liked the combo of talking with the chill music!

[@radhead]

Thank you :)

[@christopheryoung1878]

Excellent! You've made me hopeful about something I've been trying to prove about hyperboloids as it relates to the Geometric Mean. Namely, that the cross-sections are rounded triangles (using the outlining method you demonstrate) of constant widths.

[@shybound5905]

yo ive seen so many videos about shapes of constant width but none of them talked about minowski sums and meissner tetrahedrons. nice research

[@radhead]

This is exactly the reason I made this video :)

[@timacrow]

Wonderful video! Thanks!

[@fallingstones2396]

Fascinating, thank you for the demonstration!

[@googleplex7097]

This is the best video ive seen on this subject.

[@ricardombr]

This is actually a good explination, good job you shoukd have more recognicion for your efforts.

[@Funkeman]

Thank you!! This finally showed me why my Reuleaux-tetrahedron would not act the way I wanted. The animation at 4:40 showed me how to achieve it in NX. Now I soon will be printing my own body of constant width with rounded edges and corners.

[@justintaylor375]

This video should have 35 million views!

[@radhead]

thank you!!

[@kasulavineethkumar3510]

This is amazing ......keep doing such work ...oneday u will thankyourself...

[@radhead]

Thank you! I'm hoping to get back to it soon

[@rilka_li]

thank you for this video, it was so fun and your explanations were so clear! I REALLY want some shapes of constant width now lol

[@radhead]

hahaha glad you enjoyed it :)

[@chriswade9616]

This explains it so well. Subscribed, keep it going!

[@genesistyou]

passenger: "this road is soo bad" taxi driver: "no, it just from tire shape" passenger: "..."

[@owenkegg5608]

This video is wonderful! Thank you!

[@radhead]

Thanks :)

[@Tyler-ci1sb]

Why do you not have 1mil subs

[@hemojr]

I found this video while looking for a way to visualize the constant width polygons described in the great Poul Anderson's SF adventure 'The Three-Cornered Wheel.'

[@erkzneedtu]

wow quality video

[@radhead]

Thanks :)

[@Woody-ov6xk]

Your a genuine.👍👍👍

[@elijaht3452]

Nice!

[@radhead]

Thanks!

[@elijaht3452]

No prob

[@elijaht3452]

Can you explain how to make surfaces of constant width that can roll in any direction? I love your vids

[@radhead]

@@elijaht3452 In the end of the video I show a couple of solids of constant width that can roll in any direction. They were 3D printed and the models can be found on my website.

[@elijaht3452]

Oh ok

[@jorgeparra196]

Awesome video

[@radhead]

Thank you!

[@JulianMakes]

very nice video! subbed and clicked that bell :)

[@radhead]

@@JulianMakes thanks :)

[@abnatian]

It's a pity you stopped publishing videos. They are great.

[@radhead]

Thank you. I might come back to doing these some day :)

[@lucamatteobarbieri2493]

Reinventing the wheel

[@radhead]

:)

[@rin_box]

so cool

[@radhead]

Thanks :)

[@minglin8949]

awesome~!

[@okrooob]

you should have more subs

[@businessenglishlessonseslf8492]

Amazing information and fun to watch. However, to what purpose would you want to put these shapes. Are they of any practical use apart from the entertainment and of course mathematical value?

[@radhead]

They have some practical uses in niche mechanical links, I think the most famous example is the Wenkel engine.

[@izaiasmurati5499]

Gostei muito da matéria. Gênial 🔟

[@radhead]

obrigado

[@rivkanahmani3355]

ממשיך את דרכו של אבא. כל הכבוד!!

[@shaunteaches]

Could you share a link to the drawing tools you use? I am never happy with the compass tools o find.

[@radhead]

I believe it's a simple steadler compass, if that's what you mean

[@chrisg3030]

At 1:15 it looks as if the vertex of the Reuleaux triangle in touch with the plane is motionless in the sense of remaining at exactly the same point on the plane, and acting as a pivot for the roll. In a continuing roll this will only last for a short time and will be followed by the adjacent arc contacting the plane, until the next vertex does the same thing. How long does the vertex remain motionless? In the case of an ordinary straight sided triangle ABC rolling to the right, this would seem easy to answer. Start with A as the apex and side BC flat on the plane and start to roll. C is the pivoting vertex at rest on the plane, and will stay there until CA is now flat on the plane and only start to move thereafter. A rolling circle on the other hand never has any point on its circumference at rest on the plane. Is this the case with the Reuleaux triangle too? Just that the forward motion of a vertex in contact the plane is very slow and doesn't easily show up? The forward speed difference in a bike ride with Reuleaux wheels would still make it an alarming experience of course.

[@user-xm4hl5zx1l]

3:10

[@johanneskarlos6635]

Noice

[@radhead]

:)

[@mraihanagustn6224]

The shape reminds me of guitar's pick 😂

[@radhead]

Totally!

[@shadowaxolotl4006]

I like turtles

[@rismosch]

how they work is literally im their name. i don't get why a 5 minute video is necessary to explain that.

[@OJsY]

Nice explanation, unnecessary background music. Made it really hard to hear what you were saying.

[@alejandrocruz4469]

You speak too fast.