Ratios began as Greek logos and now shape your TV screen
Eight oranges and six lemons give a ratio of 8 to 6, which reduces to 4 to 3. That same 4:3 once described television screens, before widescreen sets moved to 16:9. Behind the humble comparison lies an ancient puzzle that troubled the Pythagoreans: some lengths refuse to form a ratio of whole numbers.
A ratio tells how many times one quantity contains another. It can be written as a to b, with a colon, or as the single value of the quotient, and equal quotients mean equal ratios. The first term is called the antecedent and the second the consequent. Stating that two ratios are equal creates a proportion, with the outer terms called extremes and the inner ones means. In physics a ratio compares quantities measured in the same unit, while quantities in different units form a rate.
More than two terms are possible. A two by four ten inches long has edges in the ratio 2:4:10, and a good concrete mix is sometimes quoted as one part cement, two parts sand and four parts gravel. A mixture of four substances in the ratio 5:9:4:2 contains 20 parts in total, so the first makes up 25 percent. Beginners often trip up by forgetting what is being compared with what: diluting juice at 1:4 makes the concentrate a quarter of the water but a fifth of the whole.
The word descends from the Greek logos, which early translators rendered into Latin as ratio, meaning reason. The Pythagoreans built a theory of ratio for numbers, yet also discovered incommensurable lengths, what we now call irrational numbers, which undermined its use in geometry. A theory free of that assumption is probably due to Eudoxus of Cnidus, while Euclid's Elements gathered results from earlier sources.
Converting ratios to decimals makes comparison easy, provided width is always measured against height. Old televisions at 4:3 come to about 1.33, widescreen sets at 16:9 about 1.78, and a popular cinema format stretches to 2.35.
Source: Ratio
