i did not dream so deeply as i did that night, when beneath the cloudless sky, the moon perched within the chill of air, an ocean dotted with infinities of stars sleep came ragged, but the dreams washed over me and pulled me deep into their undercurrent dreams of my childhood, drenched in clarity, picked…
Author: Clio
Geometry Limericks
Two circles surrounding a squareWas more than the poor thing could bearIt made itself fetal‘Til planar was hedralCylindrical nets are a snare! Isometry! Great celebration!But tragedy followed elation,When off of the gridThe image got slid.The pre-image, lost in translation. A circle can hardly affordTo argue with segments, good Lord!When a disc meets a lineIt is…
A trio of math limericks
Inspired by Math with Bad Drawings, here a trio of my own limerick creations: Two circles surrounding a square Was more than the poor thing could bear. It made itself fetal ‘Til planar was hedral. Cylindrical nets are a snare! Isometry! Great celebration! But tragedy followed elation, When off of the grid The image got…
The Color of Strawberries and the Curse of Knowledge
A recent meme asks: What color are the strawberries? Most people will see the strawberries as being red even though there is no “red” pixel in the image. Our minds fill in the red because of our experience with strawberries, and because we can tell the entire image has a blue filter. There is an…
Transformations as Functions
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…
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…