The tutor tackles an age-old proof in a new (to him, anyway) manner. A famous theorem of number theory goes like this: For the integers a and b, there exists a solution with integers x and y to ax+by=1 if …
Math: number theory: linear combinations that sum to 1 Read more »
The tutor shows that yesterday’s formulas to generate Pythagorean triples are valid. In yesterday’s post I showed a way to generate Pythagorean triples x, y, z from an odd number n: x n y (n²-1)/2 z (n²+1)/2 Let’s make sure …
Math: Pythagorean triples: proof of yesterday’s generating formulas Read more »
The tutor continues his discussion about Pythagorean triples. Back in my January 7, 2016 post I brought up Pythagorean triples, which are all-integer solutions to x² + y² = z² The equation above is based on the familiar a² + …
Math: number theory: a formula for generating Pythagorean triples Read more »
The tutor discusses the existence of an Euler circuit in a graph. An Euler circuit is a route through a graph that travels every edge exactly once, then ends where it started. If a graph is connected, with every vertex …
The tutor brings up a useful command for Windows. The 2015-2016 academic year over, I’m looking into the Windows 10 upgrade. Today I began gathering information: For example, when was Windows 7 installed on this computer? Searching the internet, a …
Home Computer Use: Windows: Operating system install date Read more »
The tutor looks into a simple layout technique. In web design, vertical centering is often desirable. Here’s a quick example: Hello! This text is vertically centered. See the code below. <div style=”height:11em; display:table-cell;vertical-align:middle; background-color:LightGreen;color:white; font-size:150%”><div> I’ll mention other web …
The tutor shows a way to add a style sheet to a WordPress site. There are several ways to add a style sheet to WordPress. Herein, I’ll show how I’ve done so. Let’s imagine the div below is meant to …
WordPress blogging: Adding a style sheet to WordPress Read more »
The tutor offers a way to view your history when it’s not showing. I love Firefox; it’s the browser I use with my Linux (Ubuntu) computers. Yesterday I clicked, at the top, History. A drop-down menu appeared, showing websites I …
Web browsers: Firefox: Show All History not quite working? Read more »
The tutor shares a solution to a problem from Grimaldi’s Discrete and Combinatorial Mathematics. Last night I encountered the problem (p. 481) that paraphrases as follows: Imagine a car takes two spaces, a motorbike one. Find a recursive function that …
The tutor shows another jQuery function: css() Click me for css() demo:) This text and background will both change color. Click me to reset:) The jQuery code that changes the text from ordinary to white on red: $(“#p_jun_20_2016”).css({“color”:”rgb(255,255,255)”,”background-color”:”rgb(150,10,10)”}); …