Feb
13
comment Finding the area of a circle given the inscribed figure inside it
I think this is simpler. If we arrange the triangles in this alternating manner and call the vertexes of the hexagon $A,B,\ldots,F$ then $A,C,E$ is an equilateral triangle with $AC=\sqrt{3}r$. $M$ is the center of the circle and $\angle(A,M,C)=\frac{2 \pi}{3}$ and so $\angle(A,B,C)=\frac{2 \pi}{3}$. Using the law of cosine we get ${AC}^2=1^2+2^2-2 \cdot 1 \cdot 2 \cdot \cos{\frac{2 \pi}{3}}=7$. So $3r^2=7$
Feb
12
comment If a is an arbitrary integer, then 6|a(a^2+11)
using Maxima makelist(mod(a*(a^2+11),6),a,0,5); gives [0,0,0,0,0,0]
Feb
10
comment Show that $x^4 + 8$ is irreducible over Z
@neofoxmulder No, he picked $x=9$ for the polynomial $x^4+8$ because $9$ is greater than all coefficients of the polynom. Also the coefficients have to be not negative to apply Cohn's test. For the polynomial $x^3+1$ you have to select an $x \ge 2$ for Cohn's test.
Feb
3
comment proving zeros of a polynomial are not real
see math.stackexchange.com/questions/494243/… there I use Sturm's theorem to show this. This method is straightforward and is implemented in some CAS (e.g. Maxima) to find the numbers of real roots in an interval
Feb
2
comment A dynamic dice game
I think this is the same question as math.stackexchange.com/questions/661166/…
Feb
2
comment What is a good strategy for this dice game?
I think this is the same question as math.stackexchange.com/questions/660523/a-dynamic-dice-game
Feb
2
comment What is a good strategy for this dice game?
@String I see no reason to assume that they don't count
Feb
2
comment Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
-1 It is true that $$a^2+b^2={{a}\over{b}}\,\left(a\,b+1\right)+\left(b^2-{{a}\over{b}}\right)$$ but one cannot conclude that the remainder $b^2-a/b=0$ if one divides $a^2+b^2$ by an arbitrary number.
Feb
1
comment With a product and sum of $x$ and $y$, calculate $9x^2+15y^2$
@Piwi: This problem differs from the problem you are refering to. $9 x^2+15 y^2$ is not a symmetric polynomial.
Feb
1
comment Prime number test and Fermat's little theorem
@lab bhattacharjee: yes, that is the same as saying "$a^{p-1} \equiv 1 \pmod p$ if $p$ is a prime"
Feb
1
comment Prime number test and Fermat's little theorem
$a^{p-1} \equiv 1 \pmod p$ if $p$ is a prime: en.wikipedia.org/wiki/Fermat's_little_theorem .But there are none primes such that the equation holds, like $341=11 \cdot 31$.
Feb
1
comment Coin flipping probability game ; 7 flips vs 8 flips
@David Richerby: You are right, I misread the OP. I will destroy my comment
Jan
29
comment How can i quickly calculate an approximation of $\sqrt[5]{192}$ with just pen and paper
Without comparing the results to the value calculated by a calculator: Which answer gives the approximation of $\sqrt[5]{192}$ to one digit?
Jan
27
comment Relative error machine numbers
I got the following relative errors for method A, B with $a$ and $b$ machine numbers and method A and B for $a$ and $b$ no machine numbers. But maybe I did some mistakes. $$3 \xi$$ $$\left({{b^2+a^2}\over{\left| b^2-a^2\right| }}+1\right)\xi$$ $$\left({{\left| b\right| +\left| a\right| }\over{\left| \left| b\right| - \left| a\right| \right| }}+4\right)\xi$$ $$\left({{3\,\left(b^2+a^2\right)}\over{\left| b^2-a^2\right| }}+1\right)\xi$$
Jan
26
comment Find intersection of 2 parameterized planes
$\{u_1,0,v_1\}$ and $\{u_2-1,v_2-1,1\}$ and now equate the terms. $u$ and $v$ represent arbitrary real values in a term but not the same in both terms.
Jan
23
comment How do I go about algebraic manipulation of polynomials with many terms?
the leading term is $6n^5$ on the lhs but $4n^5$ on the rhs. The constant term is $1$ on the lhs and $-1$ on the rhs. Your equation still does not hold.
Jan
19
comment Complex numbers modulus/argument question
It can be transformed to $$\frac{\text{Im}(z)}{1-\text{Re}(z)}i$$.
Jan
18
comment Complex numbers modulus/argument question
Yes, I now I see this. But then it is possible to simplify $|1-z|^2$ further.
Jan
18
comment Complex numbers modulus/argument question
why does the $|1-z|^2$ disappear
Jan
18
comment Calculation of the derivative of $e^{\cos(x)}$ from first principles
calculating the derivate uses the chain rule and the rules for $\cos$ and $\exp$. So you could try to mimic a proof of the chain rule.