Why do equilateral triangles relate to cubics
Apr 5, 2023 · I found this question talking about the relation between an equilateral triangle and cubics with three distinct real roots. Here's an image from the original post with an example: What this post s...
Notations involving squiggly lines over horizontal lines
Sep 28, 2011 · Is there a symbol for "homeomorphic to"? I looked on Wikipedia, but it doesn't seem to mention one? Also, for isomorphism, is the symbol a squiggly line over an equals sign? What is the …
Geometry notation: what does $m\angle ABC$ mean?
Jun 10, 2017 · ∠ABC refers to the physical angle itself while m∠ABC refers to its measure. There isn't any difference between these two and it is absolutely correct to use any of them...Some people just …
abstract algebra - Abelian groups and $\mathbb {Z}$-modules ...
Mar 27, 2016 · Yes, there is a bijective correspondence between Z Z -modules and abelian groups. From module to group, just forget the scalar multiplication; the module laws directly require that the …
quadratics - Newton's Identity - Mathematics Stack Exchange
Jul 10, 2021 · While reading about quadratic equations, I came across Newton's Identity formula which said we can express $\\alpha^n+\\beta^n$ in simpler forms but not given any ...
Implication Logic Truth Table Explained - Mathematics Stack Exchange
Sep 19, 2021 · The question that has bothered me for a while has been answered and closed here (Implication in mathematics - How can A imply B when A is False?) and probably many other posts. …
Compound Interest Formula adding annual contributions
Mar 15, 2016 · I'd like to know the compound interest formula for the following scenario: P = Initial Amount i = yearly interest rate A = yearly contribution or deposit added. n = the deposits will be …
What is the minimum and maximum number of eigenvectors?
May 14, 2015 · I am given the eigenvalues of a square, 8x8, matrix. They are all non-zero. I have determined that the matrix is diagonalizable and has an inverse. In one part of the problem, I am …
Hom is a left-exact functor - Mathematics Stack Exchange
Added: As witnessed by the argument above, left exactness of Hom is essentially the definition of left exactness in the abelian category of R -modules. As the comments try to point out, the importance of …
algebraic geometry - Why is a smooth connected scheme irreducible ...
More generally, locally with finitely many irreducible components is enough (each point has a neighborhood with finitely many irreducible components). The full statement is then "every regular, …