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Perfect Circle

neal.fun

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Re: Perfect Circle

#82

Post by yarg »

hinkley wrote: post #47
yarg wrote: post #44

Earlier quoted context omitted.

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.

Sure, but if you want an octagon of a specific edge length then that won't help you.

Or if you want the largest octagon that fits in a given circle (octagon of a given radius).

Re: Perfect Circle

#83

Post by culi »

ehsankia wrote: post #28

Another great neal.fun page. One feature I'd like to see is, make the user to N circles in a row and take the median score or something. Right now you can just spam hundreds and take your top score, but it doesn't really reward consistency.

A consistency reward is a cute idea. It's like "I can't draw your definition of a perfect circle, but I can draw my perfect circle"

Re: Perfect Circle

#86

Post by yarg »

hinkley wrote: post #69
madcaptenor wrote: post #57

Earlier quoted context omitted.

They are! But the octagons you draw that way aren’t regular (basically because sqrt(2) is irrational)

You can get pretty close with a pencil and a ruler though, if you have the right diameter of mechanical pencil. If you place the ruler dead on the corners of the squares and draw the line offset that tiny little bit, the error is barely perceptible without magnification.

Throw a compass into the mix and you'll get close enough.

But you like, fall off the grid man.

Re: Perfect Circle

#87

Post by hinkley »

yarg wrote: post #86
hinkley wrote: post #69

Earlier quoted context omitted.

You can get pretty close with a pencil and a ruler though, if you have the right diameter of mechanical pencil. If you place the ruler dead on the corners of the squares and draw the line offset that tiny little bit, the error is barely perceptible without magnification.

Throw a compass into the mix and you'll get close enough. But you like, fall off the grid man.

Are you trying to square a circle? We don't tolerate that witchcraft around these parts. Now git.

Re: Perfect Circle

#88

Post by kbutler »

sixstringtheory wrote: post #49
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.

But is a square more of a perfect circle than an off-center perfect circle?

Seems like this should derive the best center point of your circle, rather than mandating the dot.

But yes, we are overthinking it...

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