Watch how 19th-century Genaille-Lucas calculating rulers work

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

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Sierra Leone is the roundest country

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

The real story behind Indiana's celebrated attempt to legislate the value of Pi

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