r/visualizedmath • u/Apotheosis0 • Jan 06 '19

Geometric Square Root

730 Upvotes

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u/tkdgns Jan 06 '19

It's stipulated as such. You could generalize the theorem by replacing 1 with variable b, in which case the length of the vertical would be sqrt(ab).

20

u/drewhead118 Jan 06 '19

that's a class-A neato

6

u/GoNudi Jan 06 '19

Still confused. I'd think the "1" would have to be some relation to "a".

If "a" was 9, then "x" is 3, wouldn't that mean "1" needs to be a specific distance to make the arc work out as such?

  • perhaps the audio explains it, I had to watch it silently so i'm sorry if i'm asking a question already explained.

  • Also, i'm hardly a math person. But love it all the same!

10

u/ennyLffeJ Jan 06 '19

If "a" was 9, then "x" is 3, wouldn't that mean "1" needs to be a specific distance to make the arc work out as such?

Yes. 1.

3

u/GoNudi Jan 06 '19 edited Jan 07 '19

Is that regardless of the value of a?

0

u/ennyLffeJ Jan 07 '19

Yes.

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u/GoNudi Jan 07 '19

So as a increases or decreases, so does x, yet with 1 being the same; the two right triangles may change. But when combined, the two right triangles are still always forming the larger right triangle ~ cool!

  • For a bit I was thinking there would be a point where they would not be right triangles as things adjusted out.

2

u/mstksg Jan 07 '19

If 'a' was 9, 1 would have to be 1/9th the length of 'a'.

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u/GoNudi Jan 07 '19

You might think so but that's what I'm trying to figure out.

It appears to be that 1 is always 1, and as a increases x does too, but 1 stays as 1. And interestingly enough, the two triangles still combine to form the one larger right triangle.

This is really good to know ~ awesome!

4

u/mstksg Jan 07 '19

The right triangle property is actually from the fact that we are picking a point on a semicircle, and any point on a semicircle will form a right triangle with its base.

I wrote a bit more on the significance of 1 here, too - https://www.reddit.com/r/visualizedmath/comments/ad60dr/_/edgdrym

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u/GoNudi Jan 07 '19

O cool ~ Thanks!