It’s weird to picture, but every point on the circle has a tangent vector which is, by definition, at a right angle to the radius vector, which is what the sides of that larger pie piece both are.
You have to think of the infinitesimally small point where the two meet.
*Regular Polygon
A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).
Note that this doesn’t preclude the existence of a square with curved sides if projected upon a sphere. But when discussing common geometry the assumption is that we are working within a single plane. If you wish to work in non-planar geometry, that must be explicitly called out in the diagram.
I’m not buying that a curved lined emerging from a straight line is ever at a 90° angle to the straight. Not at any value greater than zero, anyway.
It’s weird to picture, but every point on the circle has a tangent vector which is, by definition, at a right angle to the radius vector, which is what the sides of that larger pie piece both are.
You have to think of the infinitesimally small point where the two meet.
‘Infinitesimally’ being the key word. You keep getting closer, but you never actually arrive.
A square is a regular polygon* with 4 sides.
*Regular Polygon A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).
Note that this doesn’t preclude the existence of a square with curved sides if projected upon a sphere. But when discussing common geometry the assumption is that we are working within a single plane. If you wish to work in non-planar geometry, that must be explicitly called out in the diagram.
TIL 2 things :
Squircles are a thing.
Truncated circles are ≠ from squircles
a square is a polygon, and this is not
If you think that is confusing, this will blow your mind!
Here is the definition of polygon when I googled it, “a plane figure with at least three straight sides and angles, and typically five or more.”
That has at least 3 straight sides. It doesn’t state they all need to be straight.
I mean I heard Google results were going to crap, but it didn’t quite hit home until this moment
I am sorry, but I don’t see the third straight side.
You gotta squint a little
Don’t tell them about the special glasses
My favorite geometry is poorly defined geometry