Watch This Mathematician SPIRAL OUT!! (drawing Curves of Pursuit with a twist)

Thank you Sam Hartburn: Geogebra Goddess. We have been blessed with this beautiful file: www.geogebra.o...
My Patreon: / ayliean
I am not 100% sure who made the 3D printed thingy at the start, its been on a journey and passed through a few hands ... potentially Tom Draper? • Tom Draper - Inverting...

[@Drakonak]

huge vihart vibes here and I love it

[@Ayliean]

That is an immense compliment 🥰 glad you’re here!

[@Oltoir]

What a fantastic video! as another commenter mentioned, huge Vihart vibes! I love being "tricked" into finding geometry or maths fascinating! I like the idea of one per month, that seems doable! (and wow, will this ever be shown in maths classes I bet!)

[@ThomasGiles]

I was like, wait... is this Vihart?! Great stuff...

[@TigerWalts]

I recall from one of Martin Gardner's books (More Mathematical Puzzles And Diversions) that if you have a map and you lay a smaller similar map over the top (and within the edges of the larger map) then even if the smaller map is rotated then there will be one point on both maps that match. The Brocade points are like this but with the caveat that all corners of the smaller map must touch the sides of the larger map.

[@minimo3631]

Do you think it has something to do with the fact that overlayying a smaller map is essentialy some sort of contraction?

[@zongi700]

So fun and cool! Love the vibes :D

[@Ayliean]

Maths is more about the vibes than people think! Thanks for stopping by 💗

[@swapbriarASMR]

Now this is the bright, vibrant, hot pink math I subscribed for ^_^🌼Your love and passion for maths is too contagious! I was smiling the whole time :)

[@MrDowntemp0]

Might be intresting to use a ratio of the line instead of a fixed amount, even on regular shapes.

[@Ayliean]

Ooooh, yeah - if you do it show me what it looks like. I think it will be a curve of pursuit with increasingly more definition as you approach the centre :)

[@cheque_soto]

@@Ayliean, if you use the ratio of each line, all the inside polygons are congruent to the original one, also, the point the curves converge to is the barycenter.

[@BrickBending]

Why have I not supported you on Patreon up until now? I will correct that. You are AWESOME.

[@MagicWazam]

Great video and an amazing start of the year given your resolutions! As other pointes out, huge Vihart vibes with the spiral of knowledge. I think that's a great format for math communication, knowledge is best when you can attach it to different things and concepts, possibly in other fields, and link information and solution across your own personal "mind graph". So having a bunch of geometrical visualisations, algebraic concepts, a brief mention of the 65k+ ways you can define a triangle's center (wait, WHAT?!), with your thoughts on the naming of those points so all those concepts can stick better... All around, a lot of great choices!

[@Depressed_Dinosaur]

Sending you love from Ohio - Geometry truly is the expression of life. Your tie to nature is right on. Will see you soon on patreon. - PS - Do what you love.

[@laurihei]

"SPIRAL OUT!! KEEP GOING!!" 😄🎶

[@gwalla]

Ooo, what about a Sierpinski triangle with a spiral of pursuit in the center triangle of each iteration? That would probably look cool.

[@Ayliean]

It does look pretty cool, and if you do an alternating clockwise/anti-clockwise for the different directions of triangles it looks even cooler :) if you draw one, show me!

[@timh2859]

I bought a toy very much like that but rainbow a couple months ago. fun fact, it happens to be a good representation or visualization of a salvia trip

[@ZedaZ80]

I used to do doodles like this, but instead of straight lines, I liked to use arcs!

[@BleuSquid]

Oooof this brings back memories! I used to do a lot of "curve stitching" (I only just learned that term existed!) back in high school. I never dabbled in the nested shapes variations. I was focused more on drawing things with the resulting curves.

[@1tbs-fyi]

I attempted my first curves of pursuit square. By the end, it had gone through a square to rectangle to trapezoid to quadrilateral transformation.

[@Giantcrabz]

i used to draw these all the time in school :)

[@chimitrash]

Another one for the watch later pile, for when im not too sleepy to engage with math

[@AaronNGray]

Gosh thats wonder please do a long version with the math for the geometry please !

[@Ayliean]

Like a real time drawing and Geogebra?

[@BrickBending]

Not EXACTLY the same, but dangerously close: kzbin.info/www/bejne/mKDVgnWKhbhmj7Msi=zYjHDOXQTBNdbJEp&t=138 kzbin.info/www/bejne/p4eYmnSYeJaGa5osi=r57mMBEINvz1cYZS&t=94

[@marctelfer6159]

Since they relate to curves of pursuit, I'd have maybe gone with "points of pursuit"

[@davidalearmonth]

I thought this was a really good video! And Pentagons pay the Rentagon is awesome! Aren't they also related to the Golden Ratio? Maybe that's how they pay the rent?

[@joshuadee7423]

9:04 Please spiral more

[@DeathSugar]

I woudn't say they don't work for irregular shapes. They just maps into some regular shape by initial step and then curve in this new shape. Not as exciting, yeah. Maybe if we provide some extra symmetry/direction rules they might work as copy-paste tool, but I didn't figure them out on the spot.

[@ryanlind5239]

Ride the spiral! Rock on

[@joelneely]

Pursuit convergence points (clockwise and counterclockwise/anticlockwise)?

[@Sim-q9t]

does this relate to like...angles? it would only be the same in both directions if it was the same two angles either way, if it has 3 different angles, well it still has to do with circles. I am not good at trig.

[@LittleBeetleSy]

Maybe I would call them like "Dream points", as they are located at the end of bot clockwise and anticlockwise "chases"? Or something with deepness, because they're going deeper and deeper in the triangle?

[@AaronNGray]

Gosh the intersecting circle geometry is simple and obvious when shown.

[@AaronNGray]

The trigonometric construct to describe it is probably a lot more complex than the geometric.

[@0x0000org]

Where can one find a Link to your patreon?

[@Ayliean]

In ye olde’ description box, up there!

[@0x0000org]

Ahhh it was cleverly disguised as not a link.

[@AaronNGray]

Circlular trisection ? Tricircular intersection.

[@Ayliean]

I like these words

[@AaronNGray]

@ they are meant to be an attempt to come up with a term to describe the geometric construction but they fall short. Geometry is not really my area, I am more oriented around abstract algebra and Type Theory.

[@AaronNGray]

I use under and over as descriptive constructions so tricircular intersection over a triangular form ? Probably need honing more to be an accurate description.

[@cheque_soto]

What does the scale parameter refers to?

[@samhartburn]

It's the scale factor of each triangle relative to the one before it. From memory I think it's the linear scale factor, but would have to double check the code to be sure.

[@willemvandebeek]

Do you want to make 12 videos a year for us the audience or for the KZbin algorithm? This video was excellent and I hope it was a pleasure for you to edit this together. Honestly, I just want to watch the videos you have enjoyed creating & making. It doesn't matter to me if it is either once a month, or just one video every season of the year... Perhaps compromise, and make one great video every season accompanied with two smaller update videos to keep the 12 videos per year thing going? ¯\_(ツ)_/¯

[@jeromes624]

Did I miss something? Why are there 2 points?? I would expect 3.. "triangle"

[@phyphor]

There are two because they are created from going either of the two directions around the triangle (widdershins or clockwise), but each of the two points themselves is formed from an operation on all three points

[@Ayliean]

Yup, one for clockwise, one for anti-clockwise :)