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!:

In 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.

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Only the very first version of Tetris, by Alexey Pajitnov and Vadim Gerasimov, doled out bricks at random. The result is a pure puzzle, but one with a high likelihood of frustrating (and even theoretically unplayable) sequences. Accordingly, developers have introduced bias and ratio management to balance short-term unpredictability with long-term playability. There's even a a history of Tetris Randomizers to enjoy, with code examples to show the various approaches.

Here's the rule from Nintendo's definitive 1985 edition:

To cut down on piece floods (repeating pieces) a history check was added to the randomizer. This simple check would,

• choose a piece, • check if the piece was the same as the last, • If it was it would chose a new piece, but only once, • and whatever was the result, was the piece dealt.

This still didn't fix the problem of piece droughts, which was solved by switching to virtual "bags" of pieces in 2001's Tetris Worlds, so the likelihood of getting a piece increases each time you don't get it, and vice versa, for each bag of pieces. But now it's rather easy to predict, so what next? Things get really complicated with Tetris: The Grand Master 3 - Terror-Instinct (2005).

See also Bastet, a version of Tetris that simply calculates the worst possible piece for any given deal, and deals you it.

My doubtless-unpopular opinion is that predictability is not only fine, but desirable. In fact, the sequence of pieces should be deterministic in competitive Tetris, in a way that a beginner can understand, that an average player can predict some of the time, that a master can predict most of the time. Read the rest

It's a 2d projection of a rhombic hexecontahedron, first generated by Mathematica's namesake programming language back in the 1980s, when it was as damned close to magic as anything in computer science.

Spikey is one of my favorite logos. They went through many variations with many products, inspired by renaissance drawings and a vast selection of other influences, on their way to the one you see here, which was originally devised for Wolfram Alpha.

Founder Stephen Wolfram:

And that’s when I noticed an email from June 2009, from an artist in Brazil named Yolanda Cipriano. She said she’d seen an article about Wolfram|Alpha in a Brazilian news magazine—and had noticed the Spikey—and wanted to point me to her website. It was now more than nine years later, but I followed the link anyway, and was amazed to find this:

Yolanda Cipriano's website—with rhombic hexecontahedra, there called "giramundos"

I read more of her email: “Here in Brazil this object is called ‘Giramundo’ or ‘Flor Mandacarú’ (Mandacaru Flower) and it is an artistic ornament made with [tissue paper]”.

What?! There was a Spikey tradition in Brazil, and all these years we’d never heard about it? I soon found other pictures on the web. Only a few of the Spikeys were made with paper; most were fabric—but there were lots of them

The Story of Spikey [blog.stephenwolfram.com] Read the rest

Math 4 Love founder Dan Finkel writes:

You’ve been chosen as a champion to represent your wizarding house in a deadly duel against two rival magic schools. Your opponents are a powerful sorcerer who wields a wand that can turn people into fish, and a powerful enchantress who wields a wand that turns people into statues. Can you choose a wand and devise a strategy that ensures you will win the duel?

(TEDEd) Read the rest

Multiplying large numbers before calculators led to a number of ingenious inventions to make things easier, like these Genaille-Lucas rulers demonstrated by the fine folks at DONG.

Via manufacturer Creative Crafthouse:

In the days before calculators, methods of simplifying calculations were of much interest. In 1617 Napier also published a book describing a method to multiply, divide and extract square roots using a set of bars or rods. These became known as Napier's Bones. (avail on our website)

In the late 1800s, Henri Genaille, a French civil engineer, invented an improvement to Napier's Bones that eliminates the need to handle carries from one digit position to the next. The problem was posed by Edouard Lucas and thus the alternate name of Genaille-Lucas Rulers (or Rods).

There are also sets for division. You can get your own set online or print your own from these free files.

• Genaille-Lucas Rulers (YouTube / DONG) Read the rest

Mathematician Hannah Fry explains the "Ham Sandwich Theorem," a mathematical concept that says that even the most poorly constructed sandwich can be cut exactly in half with only one straight cut of a knife. Read the rest

The average person probably assumes that mathematics is a complete system in which all mathematical statements can be proved or disproved. The fine folks at Numberphile are ready to disabuse folks of this notion with a nice overview of Gödel's Incompleteness Theorem. Read the rest

The deceptively simple Collatz Conjecture is one of mathematics' most difficult puzzles. Alex Bellos shows off a cool rendering by Edmund Harris that looks like a beautiful life form from the sea. Read the rest

One of the most interesting series ever is Closer To Truth, which "presents the world’s greatest thinkers exploring humanity’s deepest questions." For instance: is mathematics invented or discovered? Read the rest

Ever try to move a sofa down a hallway that has a corner? The underlying math behind it inspired a math problem that's been a puzzler since 1966. Gerver's Sofa above shows the parameters: a U-shaped sofa moving around a 90-degree corner in an even-width hallway. Gerver's got the record so far, and it is likely the optimal sofa. Read the rest

Mathematician Gordon Hamilton presents a curious puzzle inspired by the art of Piet Mondrian: within a square canvas filled with rectangles that all have different dimensions, what's the lowest possible score when subtracting the smallest rectangle's area from the largest? Read the rest

When 60 Minutes profiled child math whiz Jacob Barnett, he demonstrated how he imagined numbers as shapes. Numberphile's Simon Pampena analyzed Jacob's thought process. Read the rest

Understanding advanced mathematics can change how you see the world, so prepare for an eye-opening journey into the world of fixed points, courtesy of Michael at Vsauce. Read the rest

Gonzalo Ciruelos set out to discover which country was the roundest in shape.

We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem to be.

For that reason, we have to define roundness some other way. We represent countries as a plane region, i.e., a compact set C⊂R2C⊂R2. I will define its roundness as

That's about where I tune out! Turns out the answer is Sierra Leone. Click through to see lots of mathy thingies on the screen, the runners-up, the least round countries, and the source code. Read the rest

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“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.”

Thinkgeek's Pi Fleece keeps you warm and irrational with the first 413 digits of Pi in machine-washable fleece, measuring 45"x64". Read the rest