Perfect Circle
neal.fun
neal.fun
What happens if you repeat the experiment with your left hand?
Have you tried switching hands and starting from the bottom?
Seems like this should derive the best center point of your circle, rather than mandating the dot.
But yes, we are overthinking it...
100% perfect circle is a pure math thing and can't be achieved with drawing in any way.
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.)
But you like, fall off the grid man.
Choose a corner and truncate, measure the edge length using a compass, and use that to draw the rest of the owl.
You can do it, but you end up with horizontal and vertical edges that are misaligned with the grid.
And I saw the opportunity to make a bad joke.
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.
Or if you want the largest octagon that fits in a given circle (octagon of a given radius).
%!PS-Adobe-3.0 EPSF-3.0
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This bookmarklet also "only" gets 99.9%
It was a blast to learn how to do things in canvas and as an exercise, a very fun little app to build. I'm not sure how the OP is measuring perfection of the circle, but in mine it was standard deviation of every drawn point around the centre of the page.
I encourage people to try to scaffold something like this together in canvas/JS sometime. Very fun project!
javascript:(function()%7Blet%20s%3Ddocument.querySelector(%22main%20svg%22).getBoundingClientRect()%2Ccx%3Ds.width%2F2%2Bs.x%2Ccy%3Ds.height%2F2%2Bs.y%2Cr%3Ds.width%2F3%2Cd%3Ddocument.querySelector(%22main%20div%22)%2Ca%3D0%3Bfor(let%20e%3D0%3Be%3C50%3Be%2B%2B)%7Ba%2B%3DMath.acos(1-Math.pow(60%2Fr%2C2)%2F2)%3Blet%20t%3DMath.round(cx%2Br*Math.cos(a))%2Cn%3DMath.round(cy%2Br*Math.sin(a))%3B0%3D%3De%26%26d.dispatchEvent(new%20MouseEvent(%22mousedown%22%2C%7BclientX%3At%2CclientY%3An%7D))%2Cd.dispatchEvent(new%20MouseEvent(%22mousemove%22%2C%7BclientX%3At%2CclientY%3An%7D))%7Dd.dispatchEvent(new%20MouseEvent(%22mouseup%22))%7D)()"The Pope hoped to hire a fresco artist and sent to Giotto a messenger, who asked for a competitive sample drawing. With just paper and a pen, Giotto flicked his wrist and drew a perfect circle. Vasari writes: "The messenger, seeing that he could get nothing else, departed ill-pleased...However, sending the other drawings to the Pope with the names of those who had made them, he sent also Giotto's, relating how he had made the circle without moving his arm and without compasses; the Pope…saw that Giotto must surpass greatly all the other painters of his time."
https://www.smithsonianmag.com/arts-culture/perfect-circles-...
Your limbs etc are all a collection of ball and socket/downright weirdly jointed/hinges with benefits/more weirdness. You then want to use this monstrose agglomeration (did I mention how you move the bloody things?) to draw a circle? Obviously you would decide to run a finger over a simulator of a lump with a ball in it and some on/off switches.
People are weird. Nice website though.
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 would do the same way, but using the elbow as the central/pivot point instead of the shoulder.
Then we use a "mouse"!
Fishing line attached to a collar around my shoulder could could work
—
On a completely different note, in grade school I figured out you can tie fishing line to a pencil and wait for someone to try picking it up. Then give a little jerk so it moves 10 inches or so
People react wildly differently when they suddenly see behavior their mind cannot process! One math teacher walking around the back of class literally jumped up and a gave out a loud “Ieeeyaaa!” shout.
We can react to something much faster than we can think it through
"Too slow"
"Too slow"
OK, this is clearly not meant for trackpads. I can see how I might do it reasonably in the given time with a mouse or on a tablet... but not on my laptop trackpad!! :S
Definitely not going to work with the timer
EDIT:
For those who don't know the reference: https://youtu.be/wmqsk1vZSKw
(I recall how my senior hugh school maths teacher was wizz at drawing circles, lines and other geometry on the chalkboard)
(Now my hand hurts...)