This is a mental math technique to solve non-trivial integer multiplication I picked up from one of Arthur Benjamin's talks, and is widely used by other "mathemagicians" to solve large products.

It converts an n × n multiplication problem into a n² set of single digit multiplications, arithmetically identical to the "Lattice Method". However, instead of filling the lattice first and then summing each diagonal, this method calculates each sum as soon as possible - thus you only need to keep track of the bare minimum of working data and it becomes possible to do the problem entirely in your head.

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If you have a computer running on Linux or BSD, a microphone connected to it, and a desire not to spend $50 on a very small amplifier, you can use a one line shell script to listen to yourself sing instead.

Listening to yourself through a vocal monitor gives a better indication of the pitch and timbre of your voice than just listening to yourself, as the sound reaching your ears from your mouth is affected by resonating through your head, like listening to someone talk through a bone wall covered by a wet blanket. A monitor will therefore be a more accurate reproduction of what you sound like to everyone else than "directly" listening to your own voice.

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This is a reference table for deciding what to make, or making batches of dough for later use. It was going to be part of a page on Doughs and Batters for the Cooking Reference Tables section of my old site, but I never finished the rest of the dough/batter tables, so posting this one here on it's own.

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In a similar vein to last week's post on simplifying squares, this one uses some basic algebra to make it easier to multiply numbers between 10-20:

(10 + x)(10 + y) = 100 + 10x + 10y + xy = 10(x + y + 10) + xy

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Part one of what I hope will be series of at least two articles on how different lifeforms differ.

To start off, this article will give an overview of the hierarchical classification of biological life, with a focus on the nomenclature of biological nomenclature.

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This is a simple method to make it easier to calculate squares in your head (or on paper). The key is the following equation:

x² = (x+y)(x-y) + y²

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