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Consider the first “proof” in this link but instead, start with a circle radius 2 and a square with side 4.
Then please correct me if I’m wrong, but doesn’t the “similar triangles” proof written out in this link also prove that the 2 unit circle and 4 unit square are similar?Jim-
“Proof is making obvious what was not obvious.” -Rene Descartes
I already know all that you wrote, and could have written it myself. But to a sophomore it’s all irrelevant BS. Why must such a simple idea be made so complicated?
I guess what I’m really asking is why must all students in US high schools be expected to “Prove all circles are similar” when it is obvious?
Re your simple version: “You can take two circles and move one so that they have the same center, then dilate it so they are the same size. QED”
If that’s all there is to do, then why in the world is this trivial idea a specific standard?Jim-“Prove all circles are similar” is a specific common core standard that ALL high school students are supposed to be able to do. But your reply you state “slap some Cartesian coordinates on them” and then, in my opinion, just do a bit of handwaving.
Are you saying all Euclidean geometry is now dependent on coordinates?
Most high school students, teachers ,and textbooks do not think about similarity in this way .
Traditionally, Euclidean Geometry did not depend on a coordinate system for meaning. This is new to me. When, and who, made this decision?
Jim-“Prove all circles are similar” is a specific common core standard that ALL high school students are supposed to be able to do. But your reply you state “slap some Cartesian coordinates on them” and then, in my opinion, just do a bit of handwaving.
Are you saying all Euclidean geometry is now dependent on coordinates?
Most high school students, teachers ,and textbooks do not think about similarity in this way .
Traditionally, Euclidean Geometry did not depend on a coordinate system for meaning. This is new to me. When, and who, made this decision?
