A Math Puzzle For You
Find the last two digits in this expression. It’s a big number. Desmos gives up on the 3rd seven. Desmos has already copped outScreenshot from Desmos.com. Instead, let’s look at bite-sized powers of 7. (“Bite-sized” here means “less than 2 billion.”) Below are the first 12, conveniently arranged in columns of 4.
Read full storyThe Twin Paradox Explained
How special relativity predicts time dilation, length contraction and simultaneity loss. Rocket image by OpenClipart-Vectors from Pixabay, modified by Author. [Two ships in the night. Bob sees Alice travelling to the right at half the speed of light. From Bob’s frame of reference, he is at rest and Alice’s clock is running slow. Alice’s frame of reference has Alice at rest while Bob travels to the left. According to Alice, Bob’s clock is running slow. When they meet again, who will have aged more?]
Read full storyThe Law of Sines Made Clear
Once you see a triangle this way, you can never unsee it. Do you remember the Law of Sines from high school trigonometry? You may have memorized it, but did you really get it? Did you feel it in your liver?
Read full storyA Tale of Rejection
It was the summer of 1971. I was 7 years old (almost 8, thank-you-very-much). I had just read E.B. White’s Trumpet of the Swan. Finishing a novel always brought a time of grief for me. The characters who had been alive for me during those chapters were now no more.
Read full storyThe Circle-Parabola Problem
No Calculus. No Algebra. Just Plane Geometry. Actual image of Euclid solving a problem he found on InstagramWikipedia Commons. In June 2021, Dr. Peyam (of YouTube fame) published a video of a geometry problem he found on Instagram. The solution, he says, “uses a lot of beautiful geometry and even more beautiful calculus.” (It does indeed. Check it out.)
Read full storyIn the Celestial Chorus, Earth Sings Alto
From Pythagoras to Kepler, mathematicians saw music in the motions of the planets. The Earth and Venus are altos. Mercury sings soprano and Mars, tenor. Jupiter and Saturn together provide the bass.
Read full storyThe Librarian
(Fiction: Unaccompanied Minor Serial, Part IV) David flinched when he heard a shrill voice fill the sacred space of silence. This was the Bent Fork Public Library. Once you stepped inside, you felt you mustn’t utter a sound beyond a voiceless whisper.
Read full storyFind The Fox Puzzle 🦊
You have 5 holes and 1 fox. The holes are in a line, left to right, A, B, C, D and E. The fox is in one of these holes. Fox image by Daniel Roberts / Pixabay (modified by Author)
Read full storyNever Give In
“You resign now.”The Queen’s Gambit / Netflix (Fair Use) We could take the advice of Mr. Shaibel, Beth Harmon’s mentor in Netflix’s The Queen’s Gambit. Then, hanging your Queen is a good time to resign. (I can think of two sisters who would probably disagree. What would Mr. Shaibel think of the Botez Gambit? But, I digress.)
Read full storyThat Pesky Blue-Eyed Islander Puzzle: Why the solution works when it feels like it shouldn’t
"Tell us something we don't already know!"Illustration by Author. You may already know the famous (infamous?) Blue-Eyed Islander Puzzle. Here’s my version. 99 perfect logicians are stranded on a remote island. As perfect logicians, each is able to immediately determine the logical outcome of any statement.
Read full storyA Math Puzzle Involving Infinitely-Sided Dice
Here’s the challenge. You have three infinitely-sided dice. When you roll one of these dice, you get a Real Number between 0 and 1. So when you roll three of these dice, you get a Real Number between 0 and 3. Capisce?
Read full storyDandelin’s Delightful Spheres
Dandelin Spheres.Dandelion image by Capri23auto from Pixabay modified by Author. Mathematicians have been slicing open cones since the 4th Century BC. Here, we study one of these famous cross sections — the ellipse. Along the way, we’ll discover a beautiful proof from Germinal Dandelin of the 19th Century.
Read full storyMy CPAP Machine Was Recalled
The Author with his $2400 CAD paperweightAdam Hrankowski. Have you seen The Good Place? Hypatia of Alexandria points to the 5 on her shirt. “Is this an S? Or a math?” Centuries of unencumbered bliss in Heaven have rendered her and her companions intellectual zombies.
Read full storySocial Media Before The Internet
I wrote a short article in 1976. I was twelve. It was titled The 10 Steps to Meeting Girls. Even before the Age of the Internet, I must have sensed the value of the listicle. I also had an insight into the psyche of the pre-adolescent male.
Read full storyA Bayes’ Theorem Lie Detector
Woman with 70’s hairstyle demonstrates polygraph.FBI. Here is a neat application of Bayes’ Theorem. Imagine that a professor gives her students an exam. She wants to know how likely it is than any of them cheated. But she can’t just ask them. Can she even expect students to be report honestly on an anonymous survey? (Is it really anonymous? Really?)
Read full storyIs Your Data Secure? (Opinion)
You can increase security with 2-factor authorization tied to a physical object, such as your phone.Austin Distel/ Unsplash. I was working on my computer a few weeks ago when a notification popped up on the screen. Apparently I had just purchased takeout from a restaurant in a city about 500 miles from where I live.
Read full storyIs Maths Something We Create Or Discover (Opinion)
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk. God made the integers, all else is the work of man. (Leopold Kronecker) Next time you are at a party populated by mathematicians, and there is a lull in the conversation, (although, honestly, how could there be?) stand up and ask:
Read full storyModeling an Apocalypse: How We Use Mathematics To Describe A Pandemic
This article provides general information about disease modeling. It does not include details specific to COVID-19. For detailed information on the SIR model, please see Colombo, R.M., Garavello, M., Marcellini, F. et al.An age and space structured SIR model describing the Covid-19 pandemic. J.Math.Industry10, 22 (2020).
Read full storyA Perfect Math Curriculum (Opinion)
Peter Taylor is a professor of mathematics and statistics at Queens University in Kingston, Ontario. I recently came across this brilliant statement from him:. A crucial difference between English and math curricula is that in English the books come first and the curriculum is then based on these, whereas in math, the curriculum comes first and then the books are based on that. In the first case, the books are essentially artistic; in the second case, the art is lost.
Read full storyAre We Creating Mathematical Illiterates? (Opinion)
You’ve likely seen the posts on Facebook or elsewhere. “Well, another day has passed and I still haven’t used Algebra once!” A Google search of this sentence turns up many images, including those of T-shirts and at least one tote bag. Go ahead. Copy and paste the image below. You’ll likely garner several LOL’s.
Read full story