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Interesting. Typical safe mathematical response: "At least it seems true".

An engineer, a physicist, and a mathematician are traveling by train through the British countryside. They spot a black...

I understand what you are saying also, but I made this for linear algebra students who are familiar with the parallelogram spanned by two vectors. They would take it as a given that the figure is a...

Sorry for replying so late but I was on a trip. To see where a is you just have to look up to the top. (Remember, vectors can be moved around!) Each vector appears twice in the diagram. There are...

Ok Lawrence, how is this? I routed out the walnut middle piece and replaced it with arbutus to match the removable pieces. It should now be more obvious that the areas are equal.

(Now the grain...

I do not think so. That is a pure number theory thing with no connection to geometry (since the exponents > 2) that I can see.

Sure, ask him is he has ever see it before. It is so simple, I cannot believe it is not in textbooks.

Ok, math lesson time! The determinant of a 2 X 2 matrix (ad - bc) gives the area of the parallelogram spanned by the two 2D vectors (a,b) and (c,d) which are the rows of the matrix. This is proved...