
Can't be correct?
THIS is a square.

What you have shown is a keyhole.
Quote: 100xOdds
Can't be correct?
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Those two corners are not 90 degrees near the circle area. In retrospect, none of those corners look like they are 90 degrees.
Quote: 100xOdds
Can't be correct?
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To be honestly fair, the picture looks like a chess piece ♟️. 😀
Second, the four sides of a square have to be line segments.
Quote: ThatDonGuyFirst, technically, none of the angles are "right angles"; their tangents may be right angles, but that's different.
Second, the four sides of a square have to be line segments.
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Isn't a curve a line? The equator is a straight line that curves around the globe, no?
Quote: billryanQuote: ThatDonGuyFirst, technically, none of the angles are "right angles"; their tangents may be right angles, but that's different.
Second, the four sides of a square have to be line segments.
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Isn't a curve a line? The equator is a straight line that curves around the globe, no?
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Not in Euclidian geometry. A "straight" line cannot curve.
I am not exactly sure what the "strict" definition of line is, but I am pretty sure it is something like, "A path such that, given any two different points A and B on that path, the path from A to B that has the shortest distance is entirely on the line's path."
(This does not hold true for arcs.)
Quote: ThatDonGuyQuote: billryanQuote: ThatDonGuyFirst, technically, none of the angles are "right angles"; their tangents may be right angles, but that's different.
Second, the four sides of a square have to be line segments.
link to original post
Isn't a curve a line? The equator is a straight line that curves around the globe, no?
link to original post
Not in Euclidian geometry. A "straight" line cannot curve.
I am not exactly sure what the "strict" definition of line is, but I am pretty sure it is something like, "A path such that, given any two different points A and B on that path, the path from A to B that has the shortest distance is entirely on the line's path."
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If a line extends infinitely in both directions, and we live on a globe, aren't all lines circles ?
If I start at Point A and walk in a straight line, I'll eventually end up back at the same spot.
What am I missing?
Quote: billryanQuote: ThatDonGuyQuote: billryanQuote: ThatDonGuyFirst, technically, none of the angles are "right angles"; their tangents may be right angles, but that's different.
Second, the four sides of a square have to be line segments.
link to original post
Isn't a curve a line? The equator is a straight line that curves around the globe, no?
link to original post
Not in Euclidian geometry. A "straight" line cannot curve.
I am not exactly sure what the "strict" definition of line is, but I am pretty sure it is something like, "A path such that, given any two different points A and B on that path, the path from A to B that has the shortest distance is entirely on the line's path."
link to original post
If a line extends infinitely in both directions, and we live on a globe, aren't all lines circles ?
If I start at Point A and walk in a straight line, I'll eventually end up back at the same spot.
What am I missing?
link to original post
The fact that you are not walking on a "straight line" if you are on a sphere - the line curves along the boundary of the sphere.
Think of it this way: shoot, say, a laser beam from the surface of the earth, parallel (well, tangent) to the surface. Would it go around the earth and return to you, or would it go out into space?
Quote: ThatDonGuyQuote: billryanQuote: ThatDonGuyFirst, technically, none of the angles are "right angles"; their tangents may be right angles, but that's different.
Second, the four sides of a square have to be line segments.
link to original post
Isn't a curve a line? The equator is a straight line that curves around the globe, no?
link to original post
Not in Euclidian geometry. A "straight" line cannot curve.
I am not exactly sure what the "strict" definition of line is, but I am pretty sure it is something like, "A path such that, given any two different points A and B on that path, the path from A to B that has the shortest distance is entirely on the line's path."
link to original post
d2y/dx2=0 is good enough in Cartesian, no?