Most high school geometry textbooks will say that there are four basic transformations. Three of these (translations, reflections, and rotations) are rigid transformations; the resulting copy (image) is congruent to the original version (pre-image). Here are examples (blue is the pre-image): The first example is a simple translation, which can be written algebraically…
Author: Clio
Liberal Men and Blurred Lines
I remember Bill Clinton’s impeachment, and the months leading up to it. I remember him saying emphatically, “I did not have sexual relations with that woman, Miss Lewinsky.” Even when he admitted to having had sexual relations with a subordinate in a workplace provided by taxpayers, he claimed it was a “private” matter. And the…
Uniting Against Milo: How to Practice Empathy Across the Political Spectrum
February began with University of California Berkeley canceling a planned lecture by controversial alt-Right speaker Milo Yiannopoulos following violent protests opposed to his appearance. Conservatives referred to the decision as censorship by “leftist cowards” organizing a “liberal lynch mob.” Some accused UC-Berkeley itself of censorship, even though the decision was motived by public safety, not opposition to Yiannopoulos’s…
Multiplication Table Slide Rule
Using Publisher, I’ve created a slide rule for multiplication tables (up to 10×10). To use it: — Print it out and cut along the dotted line. — Move the 1 on the bottom part to any single digit on the top strip. — Each number on the bottom strip lines up to its multiple on…
An Algebraic Proof of the Pythagorean Theorem
Discussing the properties of similar triangles today, I derived a simple proof of the Pythagorean Theorem that uses ratios. (I do not claim this is original to me; I’m sure it isn’t.) Consider the diagram, and given that \(\angle BAD\) and \(\angle ADB\) are right. \(\Delta ADC \sim \Delta BDA \sim \Delta BAC\). Due to the properties…
Bullies Playing the Victim
A recent cartoon by Conservative Glen McCoy shows newly-confirmed Secretary of Education Betsy DeVos being escorted by four faceless men in suits past a wall spray-painted with the graffito “Conservative.” DeVos was recently blocked from the front entrance of a school in Washington, D. C. The cartoon’s historical reference is to Norman Rockwell’s “The Problem…
Isosceles Trapezoids and Right Angles
In this entry, I’m going to start with a concrete problem and develop an abstract generalization. The starting problem: Given isosceles trapezoid \(ABCD\) with an altitude of 6. Point \(E\) is on \(\overline{DC}\) such that \(DE = 3\), \(EC = 8\), and \(\angle AEB\) is right. Determine \(AB\). We can solve this by placing points…
Growing Beyond the White Savior
A viral video recently circulated showing a black male teacher greeting each student in his elementary school class with a different handshake. It was praised as a teacher engaging with his students on their own terms. Shortly after, a second video emerged. I will discuss the second video, but my comments on it require some…
A Picture’s Thousand Words: Whitewashing Our Culture
It’s said that a picture is worth a thousand words. I recently saw a photograph whose context spoke volumes. A little over a week ago, Donald Trump issued an Executive Order regarding the entry of non-citizens from seven countries. Even long-term residents holding green cards were at risk of being detained at the border. In one…
Defending Truth: Winning the War on Fact
When Chuck Todd of “Meet the Press” accused Sean Spicer of spreading “falsehoods,” Presidential spokesperson KellyAnne Conway called them “alternative facts.” Social media erupted with mockery of the term, making up other wishful thinking “falsehoods.” This is the next step in the evolution on the ongoing attempt by certain portions of society to undermine the importance of…