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

“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".
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Samuel Hansen's fantastic math podcast is everything a technical program should be deep but accessible, thoughtful but funny, and free for all; the new season is on Kickstarter for a few more hours! I put in $35.
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Why does a flat pizza slice flop over unless you bend it into a curve? Thank Gaussian curvature, the 19th century mathematical principle that underpins everything from corrugated cardboard to eggshells to Pringles chips.
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Brilliant, high-speed math vlogger Vi Hart has revisited the topic of the sizes of infinities.
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India's Zetatrek citizen science initiative is online workshop starting on 19th July, where science and math hobbyists from all over the world are invited to study the original manuscripts of Sir Isaac Newton.
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