Beyond Euclid - #147
Welcome to Beyond Euclid #147, the newsletter for the best mathematics and science stuff of the week. I am Ali, and I curate cool math and science stuff every week to help you have a better week.
📰 Hello again.Here is the latest edition of Beyond Euclid, the source of good internet, for your weekend enjoyment. I think this one became also another great issue. Your support is greatly appreciated, so please like this edition, share it with friends, or consider becoming a paid subscriber. Thanks for all your encouragement!
•I am currently focused on wrestling these four intriguing questions, which provide a nice challenge for my mind. If you're seeking mental stimulation or simply want to engage your cognitive abilities, I encourage you to delve into them as well.
Q1. A teacher noticed that before class every student shook hands with 6 girls and 8 boys. The number of handshakes between boys and girls was 5 less than the number of all other handshakes. How many students were in the class?
Q2. Seven volumes of an encyclopedia are arranged in the following order: l, 5, 6,2, 4, 3,7. Arrange them in ascending order by volume number using the following operation. You may move three adjacent volumes to the beginning, to the end, or between any other two volumes without changing the order of the volumes in this triple.
Q3. Tea was poured from the same teapot into a cup with sugar in it and a cup without sugar in it. In which cup will the tea be cooler?
• My college math professor, a mentor who profoundly influenced my life, once advised us not to stress over teaching math to young children around the ages of 5 or 6. Instead, he encouraged allowing them to play games, explore musical instruments, learn sports, and delve into books. Motivated by his wisdom, I sought ways for my children to learn an instrument, though finding a suitable piano teacher was challenging. Local teachers weren't available, and online lessons seemed costly and potentially ineffective.
However, a breakthrough came when my daughter's aunt gifted her Simply Piano—a beautifully designed iPad app. I then bought her a piano. For the past six months, she's dedicated half an hour daily to practice, and her progress and happiness in learning are remarkable. Simply Piano's gamified approach offers numerous lesson pieces that make her feel accomplished, arming her with renewed motivation each day.
As I continue to watch her development, I plan to share further insights in the coming week. Simply Piano is an invaluable resource for any parent looking to nurture a child's musical journey.
• Math textbooks might be boring, but can a math textbook with cat pictures be boring? I don’t think so! Sheldon Axler is a funny math professor at San Francisco State University, and he put his cats’ pictures into his math textbook, Precalculus: A Prelude to Calculus. You can get his book here.
• Mathematicians Discover New Shapes to Solve Decades-Old Geometry Problem. The article discusses a fascinating breakthrough in geometry where mathematicians have found a way to construct shapes of constant width in high dimensions. Long considered a perplexing puzzle, these shapes behave like balls, rolling smoothly between flat surfaces despite their non-circular appearances. The discovery provides an answer to a decades-old problem posed by Oded Schramm, showing that significantly smaller constant-width bodies exist in higher dimensions compared to traditional spheres. This achievement offers new insights into geometric properties and has potential applications in fields like machine learning.
When I was teaching high school, we explored this concept by constructing Reuleaux triangles. This project stemmed from a playful inquiry I posed to my students about why manholes are circular, igniting a rich discussion about shapes of constant width and their practical uses. Through these hands-on activities, students gained a deeper understanding of geometry outside the standard curriculum, appreciating how mathematics can manifest in everyday designs and solving complex problems.
• This spontaneous synchronization video is reminiscent of the phenomenon observed in starfish, where these seemingly simple creatures manage to coordinate their movements without a central brain. Just like the metronomes on a flexible base that slowly align to a common beat, starfish tube feet exhibit an emergent pattern where neighboring feet begin to match up their steps through local interactions. This synchronization is akin to how starfish, despite their lack of a centralized control organ, manage to perform complex tasks such as galloping across the sea floor.
The article "Ever Seen a Starfish Gallop?" by Josh Cassidy delves into the intriguing mechanisms underlying this behavior. It discusses how researchers have studied starfish movement, revealing that each foot independently makes decisions, but collectively they achieve remarkable coordination. This natural phenomenon highlights how simple rules and interactions can lead to sophisticated patterns, offering insights that could inspire advancements in robotics and other fields.
• Galileo Galilei's telescope, which he made his observations based on evidence, investigations, and calculations, is not better or more advanced than the lousy, ordinary, and cheap binoculars sold for $20-30 today. Despite this, he made more tremendous discoveries.Â
• The ABC's of Triangle, Square, Circle by Ellen Lupton is a beautiful book that should be used for design and the teaching of geometry. There are so many passages in the book that are eye-opening.
• Richard Feynman is talking about very small and very big numbers.
• I added this fancy Stokke Bedbox to my bucket list for our kids because it will be a hit during our vacations! It's a clever ride-on suitcase that can also turn into a bed or leg rest on planes. Designed by Frost Produkt, it's easy to use with a top cover that opens up so the kids can get to their stuff. Plus, the cover flips over to become a handy desk, leg rest, or bed. It lets little ones sit comfortably on it while you're on the move, making travel a lot more fun and relaxing for them!
• According to a study conducted by Imperial College, adults who identify as night owls—those with a preference for evening activities and staying up late—tend to outperform their morning-oriented counterparts on cognitive assessments. This research sheds light on the differences in cognitive performance based on circadian preferences, suggesting that night owls may have an edge in tasks requiring mental acuity and problem-solving skills.
• This Endangered Species Stamp Collection made me look. Illustrator Tùng Nâm rediscovered his collection while sorting through his computer files. Each stamp features an animal, its scientific name, and the year it was named a species.
• Computer Science Laboratories made a simple interactive map that shows 15 Minute City accessibility scores for cities around the world. The 15-minute city is a concept that aims to ensure essential services are within a 15-minute walk or bike ride, reducing emissions from private vehicles and improving neighborhood safety and quality of life.
• I've always dreamt of having a day with nothing to do so I could just hit the road and drive endlessly. Imagine starting a journey from Sagres, Portugal and cruising all the way east to the Aldan River in Russia, covering a whopping 8,437 miles. If that's not enough adventure, you can keep the wheels rolling to Khasan, the only Russian town neighboring North Korea, bringing the journey's total to 8,726 miles. This route is known as the longest direct driving path on the planet. Driving it non-stop would take about six days and 19 hours. It's the ultimate road trip, one for the books!
• Northwestern University researchers have made a groundbreaking discovery explaining static electricity. They found that varying forces on different parts of a sliding object lead to electrical charges that generate current. This discovery, inspired by ancient observations from Thales of Miletus, clarifies why rubbing objects produces static electricity. The insight reveals that the front and back of a sliding object experience different forces, causing electrical charge buildup and leading to static shocks, like when you pet a cat. Understanding elastic shear, where materials resist sliding and produce charges, played a crucial role. This advancement has practical uses, such as reducing industrial fire risks and improving the uniformity of pharmaceutical dosing.