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Dec
23
accepted What is $\frac{1}{1+\sqrt[3]{2}}$ in $\mathbb{Q}(\sqrt[3]{2})$?
Dec
23
awarded  Socratic
Dec
22
comment Show $a^2 + b^2 + 1 \equiv 0 \mod p$ always has a solution if $p = 4k+3$
Homomorphism. Then pigeonhole.
Dec
22
accepted Show $a^2 + b^2 + 1 \equiv 0 \mod p$ always has a solution if $p = 4k+3$
Dec
22
asked Show $a^2 + b^2 + 1 \equiv 0 \mod p$ always has a solution if $p = 4k+3$
Dec
22
asked What is $\frac{1}{1+\sqrt[3]{2}}$ in $\mathbb{Q}(\sqrt[3]{2})$?
Dec
22
accepted Does $f''(0^+)=f''(0^-)$?
Dec
22
comment How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?
I found this similar problem math.stackexchange.com/questions/867676/…
Dec
22
asked Does $f''(0^+)=f''(0^-)$?
Dec
22
comment In Euclid' s Elements, why is $\frac{\sqrt{a^ 2 - b^2}}{a}$ important in the definition of “apotome”?
There's two definitions. The apotome which requires $( \frac{a}{b})^2 \in \mathbb{Q}$ - that rules out a lot of numbers - and confusingly, the first apotome which involves the ratio $ \sqrt{1 - (\frac{a}{b})^2} \in \mathbb{Q}$.
Dec
22
comment Divide a line segment in the ratio $\sqrt{2}:\sqrt{3}.$
This was used to deduce the heights of pyramids
Dec
22
comment Divide a line segment in the ratio $\sqrt{2}:\sqrt{3}.$
can you state which result of Thales is used?
Dec
22
revised In Euclid' s Elements, why is $\frac{\sqrt{a^ 2 - b^2}}{a}$ important in the definition of “apotome”?
added 34 characters in body; edited title
Dec
22
asked In Euclid' s Elements, why is $\frac{\sqrt{a^ 2 - b^2}}{a}$ important in the definition of “apotome”?
Dec
22
revised Does $(x, y) \to (e^x \cos y, e^x \sin y)$ map open sets to open sets
added 290 characters in body
Dec
22
revised How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?
deleted 144 characters in body
Dec
22
answered Does $(x, y) \to (e^x \cos y, e^x \sin y)$ map open sets to open sets
Dec
22
revised How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?
added 142 characters in body
Dec
22
comment How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?
@BarryCipra See eq 3.2 arxiv.org/abs/1002.2941
Dec
21
asked How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?