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Image PostCircle I drew using straight lines (imgur.com)

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トップ新着論争中古い順Q&A

[–]juancarias 54ポイント55ポイント  (8子コメント)

You liar!, if it is made out of straight lines it is a very large polygon, not a circle :P

[–]KnowsAboutMath 13ポイント14ポイント  (1子コメント)

But it's a lot of sides. Must be a member of the Priest class.

[–]jacopok 1ポイント2ポイント  (0子コメント)

Conventionally 10000, I'd say.

[–]sillypantstoan 55ポイント56ポイント  (1子コメント)

Here's mine!

[–]onionchowder 3ポイント4ポイント  (0子コメント)

2 Pi is pretty close to 4. I'll chalk it up to rounding error.

[–]guiltypleasures 10ポイント11ポイント  (4子コメント)

Now this seems very very very regular, so I'm curious what your method was.

[–]Sir_Sp4ce 10ポイント11ポイント  (2子コメント)

I believe there is a compass hole visible in the center. Maybe he drew the circle first and then added the tangent lines. I might be wrong.

[–]cromlyngames 1ポイント2ポイント  (1子コメント)

I think that was used to layout the dots that described the start and end of the tangent lines - they are on a perfect circle too!

[–]Sir_Sp4ce -1ポイント0ポイント  (0子コメント)

Isn't math awesome :)

Edit: the phrase reads funny, idk what's wrong with it

[–]chefwafflezs 7ポイント8ポイント  (0子コメント)

OP definitely just free handed this, no rulers or compasses or anything. Not even a pencil, just burned the image in with his fingers

[–]firekil 17ポイント18ポイント  (5子コメント)

It's the top projection of a hyperboloid, a doubly-ruled surface and thus parametrizable by straight lines.

[–]Necroromancer 30ポイント31ポイント  (1子コメント)

Or to put it another way

[–]hooe 12ポイント13ポイント  (0子コメント)

I'm just gonna go ahead and make my way back over to /r/learnmath

[–]galoischop 2ポイント3ポイント  (2子コメント)

top projection

What's that? How is it different from other projections?

a doubly-ruled surface and thus parametrizable by straight lines

Sorry to belabor you with questions, but how does this work?

[–]firekil 5ポイント6ポイント  (1子コメント)

I mean you are literally looking at the hyperboloid from the top. This is what one looks like in profile: Hyperboloid. For the second part of your question, this means that every point on the hyperboloid has two straight lines passing through it.

[–]galoischop 1ポイント2ポイント  (0子コメント)

two straight lines through it

I looked this up, sorry to be unclear. I meant to ask how that implies the curve is parametrizable by straight lines. Is it because in the plane these straight lines are part of the ruling of the surface?

[–]AuraMasterNeal 4ポイント5ポイント  (0子コメント)

man, you must have a lot of time on your hands to draw infinite lines.

[–]obelisk420 3ポイント4ポイント  (1子コメント)

I think there's a long missing on the bottom

[–]Browsing_From_Work 3ポイント4ポイント  (0子コメント)

I think it's just a spacing issue. You can see one of the lines goes a bit high through the circle.

[–]Nowhere_Man_Forever 5ポイント6ポイント  (0子コメント)

This is cool and all but how exactly is this math? I get that it's "geometry" in that it is a geometric shape, but this isn't unique or particularly interesting mathematically.

[–]Necroromancer 2ポイント3ポイント  (4子コメント)

Cool. I use a similar method but animate the nodes with trig functions in Mathematica to produce gifs like this (not the best example but you get the idea).

[–]imbeethoven 8ポイント9ポイント  (1子コメント)

Isn't that an old Windows screen saver? haha

[–]Necroromancer 1ポイント2ポイント  (0子コメント)

Dammit. Reinventing the wheel.

[–]davebees 1ポイント2ポイント  (1子コメント)

link to tumblr?

[–]Necroromancer 0ポイント1ポイント  (0子コメント)

It's mostly my photography work unfortunately, but the occasional mathsy looping gif finds its way in.

[–]rh0dium 0ポイント1ポイント  (0子コメント)

This is a Spirograph with the outer ring masked off.

[–]Goobyalus 0ポイント1ポイント  (0子コメント)

Ok, but how did you draw the circle that the endpoints of the lines are on?

[–]Angry_Table_Flipper 0ポイント1ポイント  (6子コメント)

Non-math/Engineer here - Isn't this basically the equivalent of drawing infinite number of lines perpendicular to a point at a fixed distance?
Or drawing a whole bunch of tangents and the circle just magically appearing?

[–]juancarias 8ポイント9ポイント  (5子コメント)

It is just a polygon with many many sides. You can count them, if you have the free time.

[–]nottomf 0ポイント1ポイント  (0子コメント)

I counted 116.

[–]OfficialCocaColaAMA -1ポイント0ポイント  (3子コメント)

So is a circle that you see on a computer screen.

[–]2four 1ポイント2ポイント  (2子コメント)

Only because of aliasing due to resolution limits on our displays. Internally, the computer uses the same old r2 = x2 + y2

http://www.cs.uic.edu/~jbell/CourseNotes/ComputerGraphics/Circles.html

Edit: /u/ENelligan is correct in saying there are other limitations to drawing a circle with a computer, including the limitation of a finite number of calculations done within a finite precision set.

[–]ENelligan 1ポイント2ポイント  (1子コメント)

With a finite set of rational values. So, a polygone.

[–]2four 0ポイント1ポイント  (0子コメント)

Yes, you're right, I should have said that too. Limitations also come from the need to represent a circle well and without computational hardship.

I suppose I'm optimistic, because while we cannot represent a perfect circle, a computer still constructs a circle from points in r2 = x2 +y2 , instead of actually constructing a polygon. Purity of origin instead of purity of construction is what I'm interested in here.

[–]cappehh -1ポイント0ポイント  (3子コメント)

Does this answer the question: how many sides does a circle have?

[–]xx0ur3n 6ポイント7ポイント  (0子コメント)

No

[–]Nowhere_Man_Forever 0ポイント1ポイント  (0子コメント)

One side.

[–]AuraMasterNeal -3ポイント-2ポイント  (0子コメント)

The same number as the number of licks it takes to get to the tootsie roll center of a tootsie pop.