Mathematician, artist, and engineer George W. Hart of "Möbius strip bagel" fame has recently been playing with a laser cutter to create head-spinning warped-grid jigsaw puzzles. He came up with an algorithm to generate the initial patterns but "the real fun is step 2," he says, "using a geometric transformation to warp things."
Here's a good video that shows how the increase in the number of Covid-19 follows an exponential growth curve. Each day, says 3Blue1Brown, the number of coronavirus cases is "between 1.15 and 1.25 of the number of cases the previous day."
3Blue1Brown writes: "While this video uses COVID-19 (aka the Coronavirus) as a motivating example, the main goal is simply a math lesson on exponentials and logistic curves. If you're looking for a video more focused on COVID-19 itself, I'd recommend taking a look at this one from Osmosis:"
On Vsauce2, Kevin Lieber explains the mathematical magic that enables mentalists to confound audiences by correctly guessing the number they've picked. Even though I know how it's done, it still confounds me.
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Sure, you can count them. I did, and, er, I missed a few. Or you can take one of the approaches suggested by the mathematics professors that Andrew Daniels interviewed in Popular Mechanics:
“I would approach this just like one approaches any mathematical problem: reduce it and find structure,” says Sylvester Eriksson-Bique, Ph.D., a postdoctoral fellow with the University of California Los Angeles’s math department.
This is the first use of AR/VR I have enjoyed.
Math with augmented reality
By @brzezinski_math#Mathematics #Datascience #MixedReality #AugmentedReality#IoT #5G #innovation #Education
Cc: @RenatoMunari @ingliguori@mvollmer1 @jblefevre60 @sallyeaves @LindaGrass0 @enricomolinari @GlenGilmorepic.twitter.com/Oto5WGBuSr
— Renato Munari (@RenatoMunari) January 23, 2020
Jon Cog writes, "For Christmas, mathematician Donald Knuth shared some great geeky fun. He revealed how for the last 57 years, he's been incorporating the digits of pi into the exercises of his computer programming books -- a whopping 1,700 times. And before long his annual 'Christmas Tree' lecture 'had turned into a kind of intellectual funhouse,' sharing other mind-boggling pi-related miscellanies." Read the rest
There's a scene in my novel Homeland (the sequel to Little Brother) in which the first 1,000 digits of Pi are featured; when it came time to produce the audiobook edition, poor Wil Wheaton -- the narrator -- ended up reading out Pi for four solid minutes, with some entirely understandable difficulties. Nick Land set the reading to music, creating quite a delightful little tune! Read the rest
Nathan Davis writes, "When you shuffle a deck, it rearranges the order of the cards and I got wondering what that looked like. Read the rest
Are you the driver in the lot who parks in the first spot you see? Or do you circle around and around looking for a spot by the door? Physicists Paul Krapivsky of Boston University and Sidney Redner of the Santa Fe Institute explored the mathematics of parking. The research required different equations and simulations to model the benefits of the various parking approaches. From EurkeAlert!:
Read the restIn their paper, Krapivsky and Redner map three simple parking strategies onto an idealized, single row parking lot. Drivers who grab the first space available follow what the authors call a "meek" strategy. They "waste no time looking for a parking spot," leaving spots near the entrance unfilled. Those who gamble on finding a space right next to the entrance are "optimistic." They drive all the way to the entrance, then backtrack to the closest vacancy. "Prudent" drivers take the middle path. They drive past the first available space, betting on the availability of at least one other space further in. When they find the closest space between cars, they take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers backtrack to the space a meek driver would have claimed straightaway.
So which strategy is best? As the name suggests, the prudent strategy. Overall, it costs drivers the least amount of time, followed closely by the optimistic strategy. The meek strategy was "risibly inefficient," to quote the paper, as the many spaces it left empty created a lengthy walk to the entrance.
From Toby's "Tibees" YouTube channel: "A math lesson about logarithms inspired by the legendary painter Bob Ross."
Making a solar hot-dog oven is a science fair standby, but JohnW539's CNC-milled Sundogger Instructable really digs into the classroom portion, drawing on the creator's experience as a physics/astronomy/computer science prof at Middle Tennessee State University. Read the rest
SL Huang got a degree in math from MIT, then became a martial artist, stuntwoman and weapons expert; her debut novel, Zero Sum Game, features an ass-kicking action hero called Cas Russell, who combines all of Huang's areas of expertise: Russell is a ninja-grade assassination/extraction contractor whose incredible math skills let her calculate the precise angles needed to shoot the bolts out of an armored window as she leaps towards it from an adjacent roof; to time a kick so that it breaks her opponent's jaw without breaking his neck, or to trace back the path of a sniper's bullet with eerie accuracy and return fire. Read the rest
I chanced upon Sheldon Ebbeler's hand-drawn fractals, and now plan on tattooing my entire torso, leaving only a tattered self-similar void around the navel.
Flatland is a novel by Edwin Abbott Abbott, published in 1884. It's written as a biography by "A. Square," a two-dimensional creature who is literally a living square, thinner than a sheet of paper. He lives with other two-dimensional creatures on a surface called Flatland. In the book, Mr. Square tells of his adventures in worlds of different dimensions: Pointland (zero dimensions), Lineland (one dimension), and Spaceland (three dimensions) all inhabited with creatures suited for their respective worlds. Abbott does a wonderful job of world building, explain how the society (a satire of the Victorian society) and infrastructure of Flatland works. Even though the book was written 135 years ago, I found it very easy to read. Amazon is selling the Dover edition of Flatland for less than the price of a cup of coffee. I just bought it for my daughter. Read the rest
In a delightful short video, Klara Sjöberg demonstrates the extreme and alarming freakout that you can trigger in a mechanical calculator by trying to divide a number by zero; in a followup, Lynn Grant tweets "That is why the old Friden calculators had a 'Divide Stop' key." Read the rest
Clever and wonderfully-presented: The Incredible Palindromic Hat-Trick. You may be unimpressed if you feed it small numbers. Feed it big ones! Read the rest
Rather than attempt to describe this, I'll just quote the artist verbatim:
Read the restThis is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland Mcinnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations.
A very pretty structure emerges; this might be spurious in that it captures more about the layout algorithm than any “true” structure of numbers. However, the visual effect is very appealling and requires no tricky manipulation to create.
