## Top new questions this week:

Let's consider the following variant of Collatz $(3n+1) :$ If $n$ is odd then $n \to n^2-1.$ $1\to 0.$ $3\to 8\to 1\to 0.$ $5\to 24\to 3\to 0.$ $7\to 48\to 3\to 0.$ $9\to 80\to 5\to 0.$ $11\to 120\to ... number-theory recreational-mathematics collatz-conjecture  asked by Adam Rubinson Score of 17  answered by Will Jagy Score of 1 ### "Multiply everything so far, plug into polynomial" - can these always yield primes? EDIT: I forgot how open number theory is! (I think that gets me put on mathematician probation or something.) For this question, I will accept any answer which assumes "standard conjectures" ... number-theory prime-numbers  asked by Noah Schweber Score of 15 ### Why does it seem more natural to think of$r$as a function of$\theta$, rather than the other way around? When teaching functions in polar coordinates, the nearly universal practice is to consider functions of the form$r = f(\theta)$. I think I have never seen any examples in which$\theta$is expressed ... algebra-precalculus functions polar-coordinates  asked by mweiss Score of 12  answered by user2661923 Score of 2 ### Are these equations "properly" defined differential equations? Are these equations properly defined differential equations? Modifications were made to a deleted question to re-focus it Intro Recently, in this answer I figure out that the following autonomous ... ordinary-differential-equations partial-differential-equations physics mathematical-modeling finite-duration  asked by Joako Score of 12 ### The coupon collector's most collected coupon Suppose a coupon collector is collecting a set of$n$coupons that he receives one-by-one uniformly at random. If the collector stops exactly when the collection is complete, we know the expected ... probability combinatorics expected-value coupon-collector  asked by Brocellous Score of 11  answered by Sangchul Lee Score of 8 ### Prove$\sum_{i,j:i<j} μ(E_{i} \cap E_{j} )=\infty$. The problem is: Assume that$(X,\mathcal{A} , μ)$is a finite measure space (i.e.,$μ(X) < \infty $) and the sequence of sets$E_{j}\in \mathcal{A}$satisfies$\sum^\infty_{j=1} μ(E_{j} )=\infty$.... real-analysis measure-theory  asked by rose Score of 11  answered by Robert Israel Score of 8 ### Understanding Legendre transform (and convex conjugate) I am learning convex analysis on my own and I would appreciate some help. I know that convex conjugate is the generalization of the Legendre transform. I also know the formula known for Legendre ... real-analysis convex-analysis legendre-transformation  asked by Pegi Score of 11 ## Greatest hits from previous weeks: ### A loss and gain problem This is a very simple but confusing puzzle. A customer buys goods worth$200$rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The lady gives him a$1000$... puzzle  asked by constantlearner Score of 7  answered by fgp Score of 8 ### How many even numbers of four digits can be formed with the digits 0,1,2,3,4,5 and 6 no digit being used more? My attempt to solve this problem is: First digit cannot be zero, so the number of choices only$6 (1,2,3,4,5,6)$The last digit can be pick from$0,2,4,6$, so the number of choices only 4 Second ... combinatorics  asked by akusaja Score of 4  answered by akusaja Score of 2 ### How to calculate the area of a 3D triangle? I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ... triangles 3d area  asked by iamgopal Score of 51  answered by Vafa Khalighi Score of 45 ### Proof of triangle inequality I understand intuitively that this is true, but I'm embarrassed to say I'm having a hard time constructing a rigorous proof that$|a+b| \leq |a|+|b|$. Any help would be appreciated :) inequality absolute-value  asked by ivan Score of 67  answered by k.stm Score of 122 ### Which way is length and which way is width? I hear people refer to the dimensions of things as "$2$by$4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). ... geometry terminology  asked by David Score of 15 ### Inverse of the sum of matrices I have two square matrices:$A$and$B$.$A^{-1}$is known and I want to calculate$(A+B)^{-1}$. Are there theorems that help with calculating the inverse of the sum of matrices? In general case$B^{-...

linear-algebra matrices inverse
 asked by Tomek Tarczynski Score of 179

### Is a matrix multiplied with its transpose something special?

In my math lectures, we talked about the Gram-Determinant where a matrix times its transpose are multiplied together. Is $A A^\mathrm T$ something special for any matrix $A$?

matrices
 asked by Martin Ueding Score of 285
 answered by Simon Markett Score of 190

## Can you answer these questions?

### Max edit distance between binary strings of length n

Given a binary string s of length $n>2$.An edit operation is a single character insert, delete or substitution. The edit distance between two strings is the minimum number of edit operations needed ...

binary dynamic-programming
 asked by Hosho Kana Score of 1

### Is a certain map $\mathbb{R}\to \widehat{\mathbb{R}}$ a homeomorphism?

I'm studying harmonic analysis, and I'm trying to understand the fact that $$\phi: \mathbb{R}\to \widehat{\mathbb{R}}: s \mapsto (t \mapsto \exp(2\pi i st))$$ is an isomorphism of topological groups (...

complex-analysis analysis harmonic-analysis topological-groups
 asked by Andromeda Score of 1
 answered by QuantumSpace Score of 0

### How many ways are there to arrange $3$ men, $3$ women, $3$ children in a circle such that they alternate clockwise in this order: man, woman, child?

Problem How many ways are there to arrange $3$ men, $3$ women, $3$ children in a circle such that they alternate clockwise in this order: man, woman, child? The seats are not numbered. My Opinion I ...

combinatorics permutations
 asked by WS Wee Score of 1
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