Fixing wall mounted towel rail to plasterboard wall
Attaching towel rail to drywall
least common multiple of $\{1,2,...,n\}$ is bigger than $2^{n-1}$ The least common multiple of $\{1,2,...,n\}$ is greater than $2^{n-1}$ for any $n \ge 3$.   I found this in a MATHEMATICA book, but I don't know how to prove this. Can you help me?  [Edit:  has a discussion of an asymptotic stronger result, but that relies on the . What else is known about this? JL] Physics history book with some math I am looking for a book explaining physics from, say, Galileo and Newton till now; the book should be written using some math, similarly to my physics books when I was at the university (Halliday Resnik). I am searching a book that take care of explaining the true "evolution" of reasoning, discoveries, experiment to prove or disprove something.  I do not like a book that gives definitions without explaining what had happened. I also like to find, on that book, explanations on how actual measurements are taken (how can we measure the speed of light, the mass of celestial bodies, the attributes of electron, and how were the measurements taken in the past - how was possible to measure the speed of light in 1700-1800?).  I am not very interested in recent theories like strings, branes.... so it is OK if these are not discussed.  I like to find a lot of discussions on concept that are related, like for instance the implications on space dimensionalities, ether non-existence, strange facts, missing explanations. How can I show that $(n-1)!\equiv-1 \pmod{n}$ if and only if $n$ is prime? Thanks. How to find a point on a line at a given distance from a given point on the same line (given the equation of the line)? You are given a point P(x,y) on a line of equation ax + by + c = 0. I want another point, Q(a,b) on the same line which is at a distance d from P. There will be two points. I want to find both and know which side of P each one lies.  There are related questions in this forum, but I didn't get what I am exactly looking for. Sorry for beating around the bush, and thanks for any help... Please give me an elaborate explanation. Thanks once again!!! Track next Socratic badge progress Just got the  on StackOverflow and, since it can be awarded multiple times, wanted to start tracking progress to the next one, but, the badge is not shown in Available badges to track anymore:    Is it possible to track already awarded badges that can be awarded multiple times? How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$? I'm wondering how to approach duct work, piping, and wiring? In the past, I have used the spin tool to make corners, but I find it very cumbersome. How do you do duct work and piping? I have seen people use curves, but I find it's hard to get straight 90 degree angles or just uniform angling across the whole model. It's also hard connecting piping together if they started from different locations. Here's some reference: Even/Odd Binomial Coefficients I was wondering if there's a nice general solution for the following problem:  How many numbers in the $n^\text{th}$ row of Pascal's triangle are even? How many are odd? Applescript run from menu bar? Proof of triangle inequality Database connection close Is there any method to close connection similar to  for  in WordPress?  Is it not necessary to close connection for global $wpdb? What were the rules for capitalising nouns in the 17th and 18th centuries? It seems to have been common practice in the 17th and 18th centuries in English-language sources to capitalise the first letters of nouns, as in  At which Time he prov'd himself the Noah's Dove, that finding himself no Rest anywhere, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his mouth. —  (1685)  Most original sources I can find on the web have used modern rules for capitalisation, so I have a few questions:  Was the practice used for all nouns (Note mouth isn't capitalised in my quotation above.)? When did this practice begin? When and why did it end? How to start a background process in Python? Seeking options for Spatial ETL (Extract, Transform, Load)? I am interested in the pros and cons of various spatial ETL (extract, transform, load) tools.  If you have used the items listed here (or add your own), I seek your opinions and experiences.  In particular I would like to see usability comparisons of:    (proprietary)  (proprietary, subset of FME features)  (open source)  (open source)  (I don't know that it is truly ETL, but more of a file translation toolset) Any additional lot listed   There is no need to give a review of ALL software mentioned.  If you are experienced with even one then that will be very beneficial in making a decision about which direction to go.  Example: I am looking to create a schema conversion function that will allow me to select the input layer, create a translation, and output to a new, pre-defined schema.  Optimally, after creating the translation script, I would like to have an interactive form where I can "map" fields in my input layer to the output layer (ie- The output layer will have a field called "Address", what is it called in the input layer?)  Some were mentioned in the Q&amp;A at   And here are a couple of related articles that I found. I want to create posters for my poster presentation on a conference. What tools or LaTeX classes are available for preparing posters ? What is the ideal data type to use when storing latitude / longitude in a MySQL database? Bearing in mind that I'll be performing calculations on lat / long pairs, what datatype is best suited for use with a MySQL database? Between you and ("me" or "I")? Is it correct to say "between you and me" or "between you and I"?  I am not a native English speaker, so please bear with me. What should I do if a user posts sensitive information as part of a question or answer? I've observed several incidents where users inadvertently posted detailed, sensitive information. For example, a Server Fault user who posted a question with working login credentials to his actual production server, or the Stack Overflow user who posted actual medical records as example data for his question.   What should be the procedure for handling such cases? How is every subset of the set of reals with the finite complement topology compact? While we know that every finite set is compact, how to prove that every infinite subset of $\mathbf{R}$, the set of all real numbers, is also compact in the finite-complement topology (also called the co-finite topology)?   What is the situation in the case of an arbitrary infinite set $X$ with the finite-complement topology? Show that $\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k. I think I have it figured and would like to see if I am on the right track. Thank you.