Wouldn’t the angles need to be interior?
also the sides must be straight
Define straight in a precise, mathematical way.
The tangent of all points along the line equal that line
Only true in Cartesian coordinates.
A straight line in polar coordinates with the same tangent would be a circle.
EDIT: it is still a “straight” line. But then the result of a square on a surface is not the same shape any more.
A straight line in polar coordinates with the same tangent would be a circle.
I’m not sure that’s true. In non-euclidean geometry it might be, but aren’t polar coordinates just an alternative way of expressing cartesian?
Looking at a libre textbook, it seems to be showing that a tangent line in polar coordinates is still a straight line, not a circle.
I’m saying that the tangent of a straight line in Cartesian coordinates, projected into polar, does not have constant tangent. A line with a constant tangent in polar, would look like a circle in Cartesian.
Polar Functions and dydx
We are interested in the lines tangent a given graph, regardless of whether that graph is produced by rectangular, parametric, or polar equations. In each of these contexts, the slope of the tangent line is dydx. Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ. Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.
From the link above. I really don’t understand why you seem to think a tangent line in polar coordinates would be a circle.
Polar coordinate straight
Kinda forgot the sides being parallel part. Like missing a step in assembling IKEA furniture, its not gonna turn out right.
Also pretty sure definition of a shape requires only one enclosed or contiguous area.
This one is enclosed and contiguous though, the lines of the triangle end where the circular line starts. (The rest is just a drafting residue.)
No, it is 2 contiguous regions. The line of separation is the bounding line of a “shape.”
Otherwise, the entire whitespace outside of the region is also part of the shape, as is anything it touches.
OK, imagine the space outside of the shape is black, or see through or whatever.
Well then the line of separation means nothing and then you’ve lost two right angles to the contiguous void.
Why? Does a cube floating in the void not have angles?
Without a distinction of where the cube begins or ends it does not because there is no cube and there are no angles.
