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Wouldn't the angles need to be interior?
They are all interior to the meme
This meme seems to be in a 16:9 ratio making it a rectangle.
also the sides must be straight
It's 2024 now... Not everyone has to be straight anymore!
If you want to claim you are a square, you need.
WOW! just wow, do you hear yourself?
Hi.
It's actually illegal
Believe it or not, straight to jail.
Polar coordinate 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.
Sorry that’s not what I’m saying.
I’m saying a line with constant tangent would be a circle not a line.
Let me try another way, a function with constant first derivative in polar coordinates, would draw a circle in Cartesian
Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ
I think this part from the textbook describes what you're talking about
Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.
And this would give you the actual tangent line, or at least the slope of that line.
But then your definition of a straight line produces two different shapes.
Starting with the same definition of straight for both. Y(x) such that y’(x) = C produces a function of cx+b.
This produces a line
However if we have the radius r as a function of a (sorry I’m on my phone and don’t have a Greek keyboard).
R(a) such that r’(a)=C produces ra +d
However that produces a circle, not a line.
So your definition of straight isn’t true in general.
geodesic
I knew math was homophobic!
This is merely a projection of a square on the surface of a cone projected onto a plane.
This is also not a polygon. It has infinite and 2 sides at the same time.
This actually has six right angles if you include exterior ones.