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Perfect Circle

neal.fun

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Re: Perfect Circle

#43

Post by gerdesj »

MonkeyClub wrote: post #38
gerdesj wrote: post #29

One of my maths teachers was able to draw up to something like a three foot circle on the blackboard that looked very, very close to ideal every time. He would always use two arcs to do it and it was uncanny. He would whip out a metre/yard rule to do straight lines because they are much harder to do. Your limbs etc are all a collection of ball and socket/downright weirdly jointed/hinges with benefits/more weirdness.…

My middle school maths teacher (awesome guy, also had a mustache - mid 90s) taught us how to draw (large) circles on blackboards easily: Start from the bottom and go counter-clockwise full circle having your arm fully extended. After the first couple of tries, when you build up confidence through the results, the circles get very good. The trick is not moving slowly, but doing it in one go. The 3'/two ark circles he…

That's how my teacher did it too. Our arms can be loosely described as multiply pin jointed levers after all.

Then we use a "mouse"!

Re: Perfect Circle

#44

Post by yarg »

majkinetor wrote: post #27
ynfnehf wrote: post #26

By cheating with a Python script to move the mouse, I managed to get 99.9%. Seems difficult to get higher than that, perhaps due to the mouse position having integer coordinates.

I literray came here to see who is going to proclaim automation first (and in what way) :) Unsurprinsingly, it was the first comment. 100% perfect circle is a pure math thing and can't be achieved with drawing in any way.

In a similar vein, people claim it's impossible to draw a heptagon with a straight edge and ruler.

Sure, but good luck pulling of a perfect octagon either, given the limitations of pen and paper.

And there's a perfectly good approximation that'll very quickly produce a theoretical heptagon with error margins less than the thickness of a pencil.

1/7 ~= 1/8 + 1/64 + 1/512 + 1/4096

(1/n = sum(1...infinity) of 1/((n + 1) ^ i)

(A perfect heptagon requires infinitely many steps.)

Re: Perfect Circle

#46

Post by hinkley »

dxbydt wrote: post #25
pstorm wrote: post #22

Earlier quoted context omitted.

I was wondering why some circles seemed great but got low scores. To test your tip, I just made a square and got 92%

My anticlockwise circles score more than my clockwise ones. Is there some theory behind that ?

Might have something to do with the mechanics of your shoulder. Particularly if your hand is in the air, counterclockwise feels more natural than clockwise. Or at least, for your right arm.

What happens if you repeat the experiment with your left hand?

Re: Perfect Circle

#47

Post by hinkley »

yarg wrote: post #44
majkinetor wrote: post #27

Earlier quoted context omitted.

I literray came here to see who is going to proclaim automation first (and in what way) :) Unsurprinsingly, it was the first comment. 100% perfect circle is a pure math thing and can't be achieved with drawing in any way.

In a similar vein, people claim it's impossible to draw a heptagon with a straight edge and ruler. Sure, but good luck pulling of a perfect octagon either, given the limitations of pen and paper. And there's a perfectly good approximation that'll very quickly produce a theoretical heptagon with error margins less than the thickness of a pencil. 1/7 ~= 1/8 + 1/64 + 1/512 + 1/4096 (1/n = sum(1...infinity) of 1/((n + 1)…

Octagons are great fun to draw on graph paper. They're just a truncated square.

Re: Perfect Circle

#49

Post by sixstringtheory »

zamadatix wrote: post #19

As a tip: what it's really checking is for a circle centered on the dot in the middle with the radius equal to your initial click's distance from the center. You could make a mid sized perfect circle which is slightly off the center of the dot and lose to a square that fills the play area.

This is what I aimed for since that is how a circle is defined in a cartesian equation: (x − a)^2 + (y − b)^2 = r^2 where a and b are the circle’s center point xy coordinates and r is radius.
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