STEM Blog
Escher’s Art and Penrose Tiles
I nearly fell down the rabbit hole last week writing about the Golden Ratio. I tried to cram in something about the art of M.C. Escher. But then I realized that Escher’s art was so inspired by mathematics, it needed a blog of its own this week. Maurits Cornelis (M.C.) Escher (1898-1972) was a Dutch …
Art and Math: The Golden Ratio
Without mathematics there is no art. So said the Italian mathematician Luca Pacioli, who published an entire book on the subject in 1509. Entitled “De divina proportione” (Divine Proportion), Pacioli’s work was illustrated by Leonardo da Vinci. Down through the ages, the “divine proportion” has gone by many names, like the Golden Mean or the …
What are Twelve Notes Doing in the Octave?
In a memorable movie scene, a young Indiana Jones bursts into the house with news. His father holds up his hand, and Indiana obediently stops and begins counting slowly to ten. In Greek. In past times, a knowledge of Greek and Latin was an attribute of an educated person. Many teachers today encourage students to …
How to Overcome Word-Problem Dread
After teaching SAT math for a while, one learns where students are likely to stumble. Some students are confounded by inequalities and absolute values. Others are confused by “circle problems” where you have to draw in extra lines to find the measures of sides, angles, or arcs. And then there are those students who are …
Playing Under Pressure
We’ve all walked through a park and seen players at public chess tables with timers. Such time limits keep game play moving along. They also teach players to perform under pressure, ultimately developing strategic intuition which will make them better players in the future. The often-cited philosopher Bernard Suits archly defined playing a game as …
The Fabulous Fast Fourier Transform
A lot of students first encounter the sine and cosine wave in Algebra II. Teachers introduce ideas about amplitude, frequency, wavelength, and periodicity, drawing analogies to the circular motion of things like bicycle tires and Ferris wheels. By the time kids get to high school physics, all this trigonometry actually becomes very useful when we …
Teaching Our Kids to be Discerning Media Consumers
This past week, I received a distressed email from a former colleague containing a picture of the Abraham Lincoln statue – badly damaged and spray painted – in the Lincoln Memorial in DC. Current events reported in the United States were sufficient to convince my educated compatriot that this photo was real. So, I started …
Jacquard, Babbage, and Hollerith: Punch Card History
In the 1980s, before personal computers became commonplace, we used punch cards on old fashioned mainframe computers like the IBM 360. The standard size for punch cards was 7-3/8” wide by 3-1/4” high by .007” thick. They looked like a piece of stock paper with the upper right-hand corner cut off. We encoded stacks of …
Careers in Cybersecurity and the Traveling Salesman Problem
Cybercrime It is predicted to cost the global economy $5.2 trillion over the next five years. A single data breach — unauthorized access to private information – costs a U.S. company an average of $8.19 million. We all pay. The worldwide supply of cyber security professionals equipped to defend against these criminals is woefully inadequate. …
Why Should I Study Physics If I Want to Be a Doctor?
“What have you learned by taking physics?” This final homework assignment completely stymied my AP student. “What should I say?” she asked, imploringly. She had had to work really hard to do well in this class. Nothing about physics had been intuitively obvious to her. As her tutor, I had patiently explained and re-explained the …