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…
Author: Clio
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 DeVos was recently blocked from the front entrance of a school in Washington, D. C. The cartoon’s historical reference is to Norman Rockwell’s “The Problem…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…
Constructing a Tangent
I was recently asked for an elegant proof of the following problem. It’s based on a construction challenge from Euclidea. Given: Circles A, B, and C, such that point C is on circle A, point B is on circles A and C, point E is on circles B and C, and point D is on…
The Assault in Chicago and BLM’s Clear and Proper Response
This year began with a brutal, violent act: Four black adults apparently tortured a white man with special needs for several days in Chicago, livestreaming on Facebook portions of the assault. The next week, in a superficially unrelated story, a white man was sentenced to death for killing nine black people in an attack at the Emanuel…
Factorial
I am yet over rocky cliffs, briefly divining strengths — reluctance devouring temporal madness amidst hours with the id: I. — ptkh 011217
Social Anxiety and the Highly Sensitive Person: A Reflection
I recently posted a meme on my personal Facebook account admitting to having an anxiety disorder. I prefaced it with a paragraph of neurotic text criticizing the meme for being the wrong color, then faux-mocking myself for the meta-criticism. I am a highly sensitive person with social anxiety. I use humor to deflect from dealing…