Recent content by Gavran

https://ceramicartsnetwork.org/ceramics-monthly/ceramics-monthly-article/quick-tip-reconstituting-clay

Great. The formula can also be written in the form of ## (10_d-1_d)\cdot11_d\cdot11_d ##.

I get ## 1089 ##. There is a number ## a=100x+10y+z ## and there is a number ## b=100z+10y+x ## where ## a\gt b ##. ## c=a-b=99(x-z)=9\cdot11\cdot(x-z)\implies c\equiv0\mod11 ## ## (c=100x’+10y’+z’\wedge c\equiv0\mod11)\implies x’+z’=y’ ## ## c=99x’+11y’=11(9x’+y’) ## ##...

It was an honor. Congratulations, @PeroK, @Ibix, @Orodruin, @kuruman, @DaveE, @fresh_42, @Charles Link, @Baluncore, @Chestermiller, @Astronuc, @DaveC426913, @jtbell, @PAllen, @pinball1970, and @TensorCalculus.

I can solve the problem by using a combination of brute force counting and symmetry.

“Dum vivimus, discimus” or “While we live, we learn”

This is my interpretation of the problem statement in the original post.

The transposition of a complex number is the same complex number, and the conjugation of a real matrix is the same real matrix. It is obvious that the transposition of a complex number corresponds to the conjugation of its 2×2 matrix representation. ##...

The conjugation of a complex number is also a complex number. So the conjugation of a complex number twice corresponds to the transposition of its 2×2 matrix representation twice.

There is an interesting text regarding degrees versus radians on https://betterexplained.com/articles/intuitive-guide-to-angles-degrees-and-radians/. The next picture illustrates in a simple way when to use degrees and when to use radians for measuring angles.

I do not know what you are trying to say here. If you want to take any step in your life, first you have to be born.

Isaac Newton was a great physicist, and he was also a great mathematician, which made him more independent than Albert Einstein. My final answer is Isaac Newton.

There is an isomorphism between the field of complex numbers and a specific set of 2x2 real matrices where a complex number ## a+bi ## is mapped to the 2x2 matrix ## \begin{pmatrix}a&-b\\b&a\end{pmatrix} ##. The conjugation of a complex number corresponds to the transposition of its 2x2 matrix...

All right. Based on post #19, there are the next steps. $$ \frac{d}{d\phi}(8+\frac{8}{\tan\phi}+2\tan\phi)=0\implies(-\frac{8}{\tan^2\phi}+2)\cdot\sec^2\phi=0\implies $$ $$ -\frac{8}{\tan^2\phi}+2=0\implies\tan^2\phi=4\implies\tan\phi=\pm2\implies\phi=\pm63,435^\circ $$ ##...

I suppose that you use the Pythagorean theorem here. (see below) $$ \sqrt{(a+2)^2+(b+4)^2}=\sqrt{b^2+2^2}+\sqrt{a^2+4^2}\implies0=0 $$ So, there is not a unique solution. The minimum of ## S ## where $$ S=8+\frac{8}{\tan\phi}+2\tan\phi $$ you can find by equating the first derivative ##...