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Perfect Circle

neal.fun

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Re: Perfect Circle

#63

Post by anthk »

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)…

    %!PS-Adobe-3.0 EPSF-3.0 
    %%DocumentMedia: a4 595 842 80 () ()
    newpath
    300 500 moveto
    /poly {
            /side exch def
            /angle  360 side div def
           side {
           angle rotate
           720 side div  0 rlineto
            } repeat
            stroke
            closepath 
    } def
    7 poly
    showpage
Save it as figure.ps. Also, you can try "8 poly", or "1000 poly" above "showpage".

Re: Perfect Circle

#67

Post by hinkley »

whatshisface wrote: post #58
hinkley wrote: post #47

Earlier quoted context omitted.

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

If you draw the diagonal sides as the diagonals of squares, they will have the square root of two times the length of the vertical or horizontal sides.

Fair enough. But you can get pretty close if you draw a 10x10 with 4 squares on the sides parallel to the graph. Or 5x5 with 3 on each side. The former is 6% over and the latter 6% under. And if you go juust a hair outside of the lines you're dead on. Such as a pencil tip's width off of the ruler.

I just worked that out with a calculator, but I'm fairly sure I worked that out empirically while bored in math class one year. My very wise teacher put me and the other bored kid way to the opposite side of the classroom from where his chalkboard was and looked the other way when we played 'squares' in class, safely out of the peripheral vision of any of the other kids. Probably the only time I ever dared 'pass notes' in class.

Re: Perfect Circle

#68

Post by Waterluvian »

bbx wrote: post #36
Waterluvian wrote: post #33

There’s a mini game in Mario Odyssey about walking a perfect circle. This reminds me of that. It’s charming.

That challenge was surprisingly hard. Even with the couple of landmarks (I think a few small bushes). It’s weird how high the difference was between what looked like a perfect circle and what was actually expected. It was almost like an optical illusion.

I got 100% (the second moon) purely by the feel of the controller. I didn’t even look. I just started an arc and held fast. It’s amazingly difficult to walk a perfect circle.

Re: Perfect Circle

#69

Post by hinkley »

madcaptenor wrote: post #57
hinkley wrote: post #47

Earlier quoted context omitted.

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

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.
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