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bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 3 months
seen 2 hours ago

Aged mathematician


Jan
18
comment Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$.
Write down the first, second, and third powers of $\sqrt2+\sqrt3$ and observe that the fourth power is a $\Bbb Z$-linear conmbination of $1$ and these three numbers.
Jan
18
comment Proving the trigonometric identity $4\sin\left(x + \frac{\pi}{6}\right)\sin\left(x - \frac{\pi}{6}\right) = 3 - 4 \cos^2 x$
It would help for us to see how far you’ve gotten in this.
Jan
18
comment Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$.
Right you are. I find nothing inelegant in this.
Jan
18
comment Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$.
Surely, both sets contain $\sqrt2+\sqrt3$ and all its powers. I suggest that you write out the first few powers of this number, simplifying appropriately, of course.
Jan
17
comment Trisecting an angle
Numerical evidence trumps error.
Jan
16
comment An example for Liouville's theorem (1844)?
What’s the quantification? I mean, if $n$ and $p$ are given beforehand, what would it mean to “solve” the equation? Or are you perhaps speaking of a power of a different prime than the original $p$?
Jan
16
revised Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
Gave alternative argument, by factoring 5.
Jan
16
answered Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
Jan
16
comment Suggestions for a Complex Number Proof
Alternatively, you can multiply by the conjugate(s) and find $(a^2+b^2)(c^2+d^2)=0$. This is an equation in real numbers, just the working out of @Meelo’s suggestion.
Jan
15
answered Example $g\circ f=id_A$ but $f\circ g\neq id_B$
Jan
13
comment Finding eccentricity, directrix, foci of diagonal ellipse by rotating it
Sure: you need to rotate the things you found back in the opposite direction.
Jan
13
comment Is there a name for a point on the circumference of a circle?
Nicely precise. OP was, perhaps thinking of a disk, in which case one would have to speak of a “boundary point”.
Jan
13
answered Change of a basis
Jan
13
comment Find the point on the curve farthest from the line $x-y=0$.
Aha, @WillJagy, I see your point. I guess I was thinking of the problem of finding the closest (farthest) point between a general curve and the diagonal line.
Jan
13
comment Find the point on the curve farthest from the line $x-y=0$.
@WillJagy, yes, I was thinking of mentioning that too, but doesn’t it involve doing the same implicit differentiation?
Jan
13
comment why are algebraic manipulations in general derivations valid?
In most cases, an “algebraic manipulation” is just a way of writing an expression that may be different in appearance from the original, but is equal for all values of the variable-letters that appear.
Jan
13
revised Find the point on the curve farthest from the line $x-y=0$.
added 1 character in body
Jan
13
answered Find the point on the curve farthest from the line $x-y=0$.
Jan
13
comment Find the point on the curve farthest from the line $x-y=0$.
OP said he didn’t know how to plot it. Once it’s solved for $y$, that’s easy to do.
Jan
13
comment Find the point on the curve farthest from the line $x-y=0$.
You can easily solve for $y$, as $y=\root3\of{x^3-1}$.