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.

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.

also the sides must be straight

Polar coordinate straight

It’s 2024 now… Not everyone has to be straight anymore!

It’s actually illegal

Believe it or not, straight to jail.

Hi.

If you want to claim you are a square, you need.

WOW! just wow, do you hear yourself?

Define straight in a precise, mathematical way.

geodesic

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.

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.

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

I think this part from the textbook describes what you’re talking about

And this would give you the actual tangent line, or at least the slope of that line.

I knew math was homophobic!