From the book Lateral Solutions to Mathematical Problems by Des MacHale, try this problem called "Three cloves on an orange".
Given three points on the surface of a sphere, what is the probability there is a hemisphere on which they all lie?
After thinking about it, see answer courtesy of Alex Bellos at https://www.theguardian.com/science/2023/nov/13/did-you-solve-it-are-you-a-lateral-thinker
Great tips for actually learning and remembering what you just read. I'm a visual learner so having a visual representation of what I just read or listened to really helps me be a successful learner.
https://lifehacker.com/use-dual-coding-to-study-twice-as-effectively-1851010396
"Ranked choice voting is an alternative electoral system that would mitigate the spoiler effect while giving voters more voice to express themselves at the polls."
https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/
On Sunday Nov 5th most of us get to sleep in an hour when time falls back for winter. "Between 1941 and 1945, and again 1947, there was something call 'British Double Summer Time' in which clocks sprung ahead two hours." I never knew this. Did it ever spring forward to balance out?!
RIP Eugenio Calabi, died on September 25, age 100. He was known for conceiving of novel geometric objects that later became fundamental to string theory. Good read from Quanta Mag. "Needless to say, the world does not appear to be 10-dimensional — there seem to be just three dimensions of space and one of time. By the mid-1980s, however, a group of physicists had realized that the six “extra” dimensions of the universe might be hidden in a minute Calabi-Yau manifold (less than 10−17 centimeters in diameter)." #topology #physics https://www.quantamagazine.org/the-mathematician-who-shaped-string-theory-20231016/
Fun little area problem from #MindYourDecisions. Can you quickly see the area of the shaded triangle? No algebra needed!
Hey new fall term students! Please read my "Why should college students study mathematics? Here are eight reasons. At least one will strike true for you." https://www.integreat.education/OL/docs/WhyStudyMath.pdf
While not fully developed, a couple good ideas to think about. "The same is probably happening with the Apple Watch and AllTrails, and probably depends on the sampling frequency of both apps. The difference from the Coastline Paradox is that rather than talking about the scale of distance, we’re talking about the scale of time." I've noted extreme differences between AllTrail app and my Garmin watch tracking when hiking. Garmis is also pathetic at counting flights of stairs climbed. I wonder if it is the same "sampling" problem? https://medium.com/@saswatrp/experiencing-the-coastline-paradox-78808dfeb81f
Topology in real life!
"Perhaps the coolest application of the #HairyBallTheorem concerns nuclear fusion power."
"There’s a fundamental engineering hurdle when building fusion reactors: How do you contain plasma that’s 10 times hotter than the sun’s core? No material can withstand that temperature without disintegrating into plasma itself. So scientists have devised a clever solution: they exploit plasma’s magnetic properties to confine it within a strong magnetic field. The most natural container designs (think boxes or canisters) are all topologically equivalent to spheres. A magnetic field around any of these structures would form a continuous tangent vector field, and at this point we know what befalls such hairy constructions. A zero in the magnetic field means a leak in the container, which spells disaster for the whole reactor. This is why the leading design for fusion reactors, the tokamak, has a doughnut-shaped chamber. The International Thermonuclear Experimental Reactor (ITER) megaproject plans to finish construction of a new tokamak in France by 2025, and those involved claim their magnetic confinement system will be “the largest and most integrated superconducting magnet system ever built.”
"That’s #topology playing its part in our clean energy future."
https://www.scientificamerican.com/article/what-is-the-future-of-fusion-energy/
Image: This sphere is covered in small lines resembling hairs that are all combed in the same direction. Tufts on either side demonstrate the hairy ball theorem. Credit: Buckyball Design
This is a fun #trigonometry #geometry site I can't believe I've never known about before. Kind of like proofs-without-words puzzles. Scroll the table of contents and pick out a fun one! https://trigonography.com/?page_id=230 The famous three triangles problem has always been a fav of mine since there are so many methods of solution.
Attn my Calc I and Calc II summer classes: Two recent fun pertinent videos worth a view if you have time. "An unexciting video about distance derivatives" from
Stand-up Maths at https://www.youtube.com/watch?v=sB2X5l5CsNs. Check-out the linked resources in comments too particularly if you have time with family/friends 2-hr doc "Rapid Motion Through Space: An Incomplete History of Speed" at https://www.youtube.com/watch?v=NYDdHSXRQro. Also "Simple visual logarithms, hyperbolic trig, and Shape-Shifters" at https://www.youtube.com/watch?v=G0Fa5Zl-Z3c
Attn Calculus I class: Learning about instantaneous velocity this unit, you might appreciate reading this article, written for a non-calculus audience. "It’s a shame that infinitesimals fell out of favor, because they’re really useful for thinking about relative scale." https://www.salon.com/2018/01/14/what-exactly-does-instantaneous-mean_partner/
Lightning moves pretty quickly; would you call it instantaneous?
Cool real-life example of #paraboloid and #hyperbola in nature. Original post via @coreyspowell at: https://mastodon.social/@coreyspowell/110774904285735511 Page (2004) with animation: https://hubblesite.org/contents/news-releases/2004/news-2004-11.html
Want to know a bit about what courses to take to get a maths degree? Conversation happening over in reddit: https://www.reddit.com/r/math/comments/157p61o/how_to_get_a_good_undergrad_math_education/ One of the suggestions is this PDF with a nice overview and summary of courses and paths to take: https://venhance.github.io/napkin/Napkin.pdf
Fun little interpretation of relationship between #triangle's perimeter, inner radius, outer radius. Hey #geometry #triangle students, can you fill-in the steps to reorganize the equations algebraically as Dr. Cook suggests? https://www.johndcook.com/blog/2023/07/15/perimeter-radius-sides/
Weird read.
"How does it work? She fed a list of swearwords into “the Markov chain”, a #mathematical model that predicts the probability of a sequence based on previous input and figures out the chances of each letter following the one before …
A bit like predictive text? Exactly.
What the actual duck?! We know how rubbish predictive texting is at swearing. What did the code say? That the ultimate swearword was likely to begin with a “b” and end in “er”.
So it ended up spitting out banger? It was a tie between banger and ber, but Maclean noted that the first word already had lewd connotations."
ATTN brand new Trig class: The interior angle of the pizza slice emoji in the Apple pizza emoji 🍕 48.5556º, implying that the pizza was cut into a very awkward 7.4 slices. (Or that somewhere there exists another 48º slice and two corresponding 41.4444º slices) via @Cdespinosa #MathsInAction #MathsInRealLife #geometry #trigonometry
John Golden @mathhombre has put together a nice list of #MathGames. Many I've played; several were new to me. Check them out! https://mathhombre.blogspot.com/2023/07/games-before-class.html
