Spiral of Theodorus

This is a short, animated visual proof demonstrating how to construct square roots of any positive integer using the Spiral of Theodorus

Thanks!

#manim #math​​ #mathshorts​ #mathvideo​
#construction #geometry #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #spiral #theodorus #squareroot

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[CatOnACell]

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

[kathyhenry]

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

[giovanigomes]

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

[wyattstevens]

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

[X-SPONGED]

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

[plathanos]

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

[maggi_tael]

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

[quinn]

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

[amirhaayers]

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

[עמיתלרמן]

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.

[willcooper]

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

[Suo_kongque]

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

[ZzSlumberzZ]

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

[JTCF]

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!

[danielandrade]

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!

[herbertbader]

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.

[jonasvolitsa]

Even when you are not a math person, this is all the way fascinating…

[Zealzaro]

Every time I see one of these videos I understand more why Plato had written on his academy “only geometers may enter here”

[AlessandroLongo-ph]

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

[KalliJ]

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.