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8h
comment n-simplex volume and triangle.
$|a_1 \dots a_n| = det(a_1, ... a_n)$ is the volume of the n-dimensional parallelipiped formed by $(a_1, \cdots, a_n)$. You get $\frac{det(a_1, ... a_n)}{n!}$ because you are cutting out the n-symplex from it. An idea of dimonstration could be getting the volume from standard basis symplex by integrating on each vector, the result would be $\frac{1}{n!}$, then transform it to the needed simplex.
9h
revised We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
deleted 1 character in body
9h
comment We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
It does. I assume $log(N)$ is natural logarithm, $ln(N)$ notation is better.
10h
revised We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
added 45 characters in body
10h
comment We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
Suppose you have registered $n$ different dates and want to know after how many people you will increase the number of dates to $n+1$. You ask $t_i$ person its birthday date: if it's in the list you continue asking; if it isn't then you have $n+1$ different dates. The geometric distribution counts the number of people you have to ask until you have success (getting $n+1$ dates) given the probabilities.
10h
revised We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
added 180 characters in body
10h
revised We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
added 180 characters in body
10h
answered We write down the date of each person's birthday we meet (say Feb 29. doesn't exist).
12h
comment n-simplex volume and triangle.
You are welcome. If my answer is satisfiyng, then put the tick near it to accept it. Please, do it also for the answers of your previous questions.
12h
comment n-simplex volume and triangle.
$b$ is a translation vector (see $S_n(\dots)$ definition) and isn't included in the basis $(a_1, \dots, a_n)$ for the construction of the n-simplex; in other words, if you translate a figure by a vector, its n-volume doesn't change. About 1.2) Consider generic vectors $a$, $b$ centered in $O=(0,0)$, they are 2 sides of a triangle, they are also 2 non-parallel sides of a parallelogram. The area of parallelogram is the determinant of matrix made of column vectors $a$ and $b$, so the area of the triangle is half cutting on diagonal of the parallellogram.
13h
answered n-simplex volume and triangle.
14h
comment How to show convergence of $\sum_{n=1}^{\infty}\log(1 + \frac{1}n)$?
Hint 2: $\sum{ln} = ln{\prod}$
15h
comment Quick Vector Space question using the axioms
Please, be more precise. What is $f$? Which axioms are you refering to? Show your doubts please.
2d
asked Calculate moment of inertia of Koch snowflake
2d
revised Solving an exponential equation by means of factoring
latex correction
2d
suggested approved edit on Solving an exponential equation by means of factoring
Apr
21
suggested rejected edit on Multiplication of two factors with complex numbers
Apr
18
comment Find all differentiable functions $f$ such that $f(f(x))=f'(x)$
see also this
Apr
18
comment “$111 \dots$ upto $3^n$ digits” is divisible by $3^n$
fixed, i hope it's better now; if it's not enought understandable, i'll write simpler.
Apr
18
revised “$111 \dots$ upto $3^n$ digits” is divisible by $3^n$
added 644 characters in body