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Results tagged with reference-request
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user 25619
This tag is used if a reference is needed in a paper or textbook on a specific result.
11
votes
Proofs without words
I like the tiling proof of the Pythagorean Theorem. The left image is credited to Al-Nayrizi and Thābit ibn Qurra (9th century) and the right by Henry Perigal (19th century).
1
vote
Nonvanishing of Jacobians implies global injectivity?
The answer is NO. Consider the two-dimensional example $F=(f,g)$ with
$$
f(x,y) = \sqrt{2}e^{x/2}\cos(ye^{-x})
$$
$$
g(x,y) = \sqrt{2}e^{x/2}\sin(ye^{-x})
$$
The determinant of the Jacobian matrix is …
- 664
-9
votes
Proofs without words
This is a "proof without words" by an equation, not a picture.
Three complex numbers $a,b,c$ in the complex plane form the vertices of an
equilateral triangle if and only if $~a^2 + b^2 + c^2 = ab + …