Ratios by ShapiroA

The "A series" of paper sizes is standard throughout much of the world, though not in North America where letter paper is generally 8.5 by 11 inches. What is the exact theoretical ratio (before rounding) of width to height for A series paper?

HD TV channels broadcast with what aspect ratio in the U.S., as well as in most of the world?

What word (not a proper name) has been covered by a purple rectangle in this screenshot from Wikipedia? Despite Wikipedia's officially neutral point of view, the italicized higher hints at an editorial raised eyebrow.

Click for additional information

A musical tuning system based on exact 3 : 2 pitch intervals ("perfect fifths") is commonly named after what Samian philosopher, who would presumably find the modern system of equal temperament as loathsome as the answer to Question 1?

Pareto's Law is sometimes glossed as "20 percent of the population has 80 percent of the wealth". Suppose this is the case. What is the ratio of per capita wealth for members of the top 20% to per capita wealth for members of the bottom 80%?

The ratio test, traditionally taught in third-quarter calculus, is used to determine whether a series does what?

Per the cover art on Michael Ruhlman's Ratio: The Simple Codes Behind the Craft of Everyday Cooking, for what should you use a ratio (by weight, not volume!) of 3 parts flour : 2 parts fat : 1 part water? Your smith can attest that this basic recipe works beautifully, but do add a little salt, and be sure to keep your ingredients cold.

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

This is a classical definition of what is now commonly known as the golden ratio. Mathematically, this ratio is Φ:1, where Φ ≈ 1.61803 to five decimal places. Give the square of Φ to five decimal places. (No calculators!)

Per the CIA World Factbook, the six countries whose human populations have the highest sex ratios (male to female) -- ranging from 1.18 to 3.39 -- all border what body of water? Note: None of these countries have particularly unusual sex ratios at birth.

":" : "is to" :: "::" : ??

This system of planetary gears consists of a stationary outer "ring" gear, a central "sun" gear with 18 teeth, three "planet" gears with 12 teeth each, and a Y-shaped "carrier". What is the ratio of turns made by the sun gear to turns made by the carrier?

Click for additional information

What is the ratio of shaded area to total area in the regular octagon shown?

Click for additional information