Fun with MS Paint

I was wondering about MS paint and stumbled upon certain interesting problems. Here they are.

Problem 1: Can you draw an equilateral triangle in MS Paint?

Problem 2: Can you draw a regular hexagon in MS Paint?

Problem 3: Can you draw a regular polygon having odd number of sides in MS Paint?

Rules: You cannot use any aid to make measurements of any kind (length or angle). You can only use MS Paint (obviously). You are not supposed to use the co-ordinates to make measurements of any kind (length or angle). However, you can use the co-ordinates for precise placement of your mouse pointer.

Note by Bruce Wayne
6 years ago

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It's impossible; drawing on MS Paint requires the vertices to be lattice points, and it's a well-known result that a regular polygon that is not a square cannot have their vertices on lattice points (using that if a,b,ca,b,c are rationals and cosaπ=b,sinaπ=c\cos a\pi = b, \sin a\pi = c, then 2a2a is an integer).

Of course, assuming that MS Paint's canvas is infinitely divisible (so it's basically a plane of reals times reals), then it's the usual compass and straightedge problem.

Ivan Koswara - 6 years ago

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Read my comment below. The equilateral triangle and regular hexagon can be constructed (and should looks okay if the screen resolution and the size of the computer screen is 1:1). Only the pentagon is impossible to construct.

Adam Zaim - 5 years, 11 months ago

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In Windows 7, you can make a hexagon and a pentagon. Plus, you didn't say a REGULAR hexagon. So, problem 2 and 3 have been solved. But I don't know how to make equilateral triangle.

Adam Zaim - 6 years ago

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Problems 2 and 3 have been revised. Try them out now :P

Bruce Wayne - 6 years ago

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Heh. I knew it you meant that way. But in Windows 7, I just realized that I can solve those three puzzles easily. Okay, let's say that you do it in Windows XP. I'll try solving these problems. Because I might got it. Might. Hehe.

Adam Zaim - 6 years ago

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@Adam Zaim Can you provide your Win7 MS Paint solution for the three problems?

Bruce Wayne - 6 years ago

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@Bruce Wayne In windows 7, there are three tools. You can make a triangle, a hexagon and a pentagon by using these tools.

After choosing a tool, let's say a pentagon, while holding the shift key, you can make a regular pentagon. That will also work on other tools.

I think making a pentagon in Windows XP paint is impossible.

Adam Zaim - 6 years ago

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I think I got it. picture

Adam Zaim - 6 years ago

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err how do you draw the circles so precisely?

Ryan Soedjak - 6 years ago

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This video shows you how to make a 60 degree angle, an equilateral triangle and a hexagon. Youtube video I hope I didn't break any rules. Plus, constructing a regular pentagon is impossible in Windows XP paint.

Adam Zaim - 6 years ago

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