Month: April 2010

This just blew my mind:

[W]hat’s 27 [squared]? Of course, the brute force way to do that is to calculate 27 x 27 which is a bit of a pain because it involves doing something like 27 x 20 + 27 x 7 = 540 + 189 = 729. But there’s a much faster way.

Observe that 272 = 30 x 24 + 32. Since you probably know that 32 = 9 this means you have to calculate 30 x 24 + 9 which is relatively easy because the multiplication involves a multiple of ten which means it’s really 3 x 24 and then add a zero.

So the rule is that if you want to square number X you first round it to the nearest multiple of 10, called that X + r, and then calculate X – r (i.e. round the same amount in the opposite direction). You calculate (X + r) x (X – r) and add back the square of the amount you rounded by, r2, which will be 1, 4, 9, 16 or 25.

I convinced myself with a simpler example: 12 squared. Round down to ten and an equal amount up to 14; square the amount you rounded (2) and add it to the product: 10*14 + 2^2 = 144. Cool…

Re-nest posts:

Anyone even remotely informed about the environment and sustainable design knows that the color green is the go-to visual representation, via branding and packaging, that a product is sustainable, organic, or eco-friendly. But a fascinating article recently in The New York Times points out the cruel fact that most forms of the color green are manufactured in ways that are ecologically irresponsible, and in some cases severely damaging to the environment.

This is definitely quite ironic; I would have never guessed that the green pigment was so difficult to produce:

Take Pigment Green 7, the commonest shade of green used in plastics and paper. It is an organic pigment but contains chlorine, some forms of which can cause cancer and birth defects. Another popular shade, Pigment Green 36, includes potentially hazardous bromide atoms as well as chlorine; while inorganic Pigment Green 50 is a noxious cocktail of cobalt, titanium, nickel and zinc oxide.

Green even has a toxic history. Some early green paints were so corrosive that they burnt into canvas, paper and wood. Many popular 18th- and 19th-century green wallpapers and paints were made with arsenic, sometimes with fatal consequences. One of those paints, Scheele’s Green, invented in Sweden in the 1770s, is thought by some historians to have killed Napoleon Bonaparte in 1821, when lethal arsenic fumes were released from the rotting green and gold wallpaper in his damp cell on the island of Saint Helena.