Spiral of Theodorus

no, but this will be a great tool for drawing seashells in the future.

"Spiral of Theodorus" sounds like some maguffin from a new Indiana Jones movie

I don't think I'd be able to construct sqrt(200), except as 10sqrt(2).

The lore behind that first triangle is quite... "irrational"

Nice! finally something new to put on every image besides the golden ratio

"Do you think you could construct this by hand?" Ammonites: "I don't even need hands"

my teacher made us draw an entire page of this thing, thanks for reminding me of this traumatic experience

damn he really wanted to know if I think I could construct this by hand

I like the pacing of this short. Very contrary to the seemingly rushed speech and lack of breaks of other shorts

I heard spiral out. The TOOL fan in me has been awoken.

Once it gets bigger it kinda looks like a fancy spiral seashell. It's really pretty.

I remember learning this 9th class but couldn't fully understand it back then

There is a much simpler and non-recursive way to construct sqrt(n) using the fact that sqrt(n)=sqrt(n*1) which is the geometric mean of n,1. The geometric mean of two numbers a,b can be seen as a perpendicular to a diameter of a circle with length n+1 when the perpendicular stops when it touches the circle. In other words, you can first construct n+1, which is a pretty simple task, then bisect the segment to get the center of the circle. Then you can draw the circle, draw a perpendicular line 1 units from the end of the segment and voila your sqrt(n) is just the length of that perpendicular segment.

Sounds like a cool way to compute the square roots. Actually, I wonder how computers do that in the first... New rabbit hole, here I go!

Clearest explanation ever

Lol I actually found this by myself just doodling some triangles. Super cool that you can get measurements for basically any square root’s values this way!

My geometry teacher in high school would have us do constructions every week where we’d make a little piece of “art” using whatever formulas we were learning about at that time. This would be right up her alley 😂

then visual representation of the spiral motivates the conjecture, that the difference of the radius between the loops remain constant. Then one could draw the spiral with a pencil limited by a thread winded up around a cylinder with radius=1 in the center which is rolling off by drawing. The difference between loops therefore is constantly 2*pi.

I can't figure out the point of using the compass, since you don't show using it to find the perpendicular of your √ line. You can make this construction with just a right-angle triangle ruler for your straight edge.

Well, this is the best thing I've seen the whole day. Thank you for this amazing performance.❤