Because It’s There

By | January 8, 2016

As I have on many occasions, over the holiday hiatus I was binge-watching the British quiz show Q.I. (Quite Interesting)—Stephen Fry (although, as of next series, Sandy Toksvig) hosts four British comedians who answer extremely obscure questions, make jokes (often bawdy), and offer their own “quite interesting” factual tidbits. My favorite question from the “E” series (each season of the show corresponds to a letter of the alphabet; they are currently up to “M”) was from a show called “Exploration” and was: “Who was the first person to put two feet on top of Mount Everest?”

The answer to this question is not Sir Edmund Hillary, or even Tenzing Norgay. As we begin our exploration of who this could be, our point of departure will be…the decimal point.

Our old friend the decimal point—the dot that separates the integer from the fractional part of a number (as in 198.57)—was actually necessitated by the advent of printing. Before the printing press, medieval mathematicians and others needing to write decimal numbers would use the tradition descended from Indian mathematics and popularized by the Persian Al-Khwarizmi: place a bar over the rightmost integer, which indicated that all the numbers to the right of it were the fractional part of the number. So:

9995

would correspond to 99.95 in today’s decimal notation. (Man, it has become impossible to set a macron or overbar over a numeral in any modern word processing program.)

Al-Khwarizmi was a 12th-century mathematician who is called “the father of algebra” (that word comes from al-jabr, one of the operations used to solve quadratic equations). He introduced the notion of decimal numbers to the West, as well as another convention we still often use today, often with prices: setting the fractional part of a number in superscript with an underbar, as in $1995 for $19.95.

Another convention that was often used when writing decimals was to place a small vertical line between the integers and the tenths; once typesetting and printing were invented, the comma served this purpose admirably, and we still often see the comma used in place of a decimal point (99,95), especially in Europe. Around the same time, it began to be customary to use the full-stop (aka the period) as a decimal mark. The reason was that the comma and the period already existed in font collections, while other obscure math-specific characters did not.

The person who is often credited with first using the decimal point is Bartholomaeus Pitiscus (1561–1613), a 16th-century German mathematician, astronomer, and theologian. He used the decimal point in his highly influential 1595 book Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuous. Although Pitiscus first used the decimal point, it wasn’t until John Napier—the inventor of logarithms—following Pitiscus, used it in his 1614 tome Mirifici Logarithmorum Canonis Descriptio. Then everyone, it could be said, got the point.

It was in his book that Pitiscus also coined the word “trigonometry,” but although he named and popularized the subject, he didn’t actually invent it. Trigonometry—essentially the study of triangles (from the Greek τριγωνομετρία, or “trigonometria,” meaning “triangle measuring”)—can be traced back to 2nd millennium Egypt and Babylon, where it was used for such things as building pyramids (“If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?” would have appeared in your average Egyptian SAT) as well as making astronomical observations and measurements. It was the ancient Greeks who took trigonometry to the next level, and Hipparchus of Nicaea (180–125 BCE) is considered “the father of trigonometry.”

So what is trigonometry anyway? For those who don’t recall high school math, it is the study of the relationships of the lengths and angles of triangles. All the angles of a triangle add up to 180°, so if you know that one angle of a triangle is 90° (that is, it’s a right triangle) and you know the value of one of the other angles, then it’s easy to find the value of the third angle. Using known values of angles, and the length of one of the sides of a triangle, the lengths of the other sides can be calculated using the trigonometric functions sine, cosine, and tangent, which describe ratios of the lengths of various combinations of sides for a given angle. There are also the reciprocal functions of sine, cosine, and tangent, which are, respectively, cosecant, secant, and cotangent, and inverse functions arcsine, arccosine, and arctangent.

Now, I mentioned earlier that trigonometry was used in pyramid building, but what else might it be used for? Think large structures…like mountains. Where do you find large mountains? The Himalayas, of course. And this is just where the Great Trigonometrical Survey was conducted. Launched in 1802 and spearheaded by British soldier, surveyor, and geographer William Lambton, its goals were to a) demarcate British holdings in India and b) determine the locations and heights of the great Himalayan peaks.

The Great Trigonometrical Survey was no easy feat, and took decades to complete. Lambton was replaced as head of the project in 1823 by Welsh surveyor George Everest, and in 1831, Everest hired a brilliant 19-year-old Indian mathematician named Radhanath Sikdar (1813–1870). Sikdar and Everest worked closely for many years, Everest calling Sikdar a “mathematical genius.” In 1851, Sikdar was promoted to Chief Computer and was tasked by Everest’s successor, Andrew Waugh, to calculate the height of one particular mountain, variously called Peak XV (the British), Sagarmāthā (the Nepalese), and Chomolungma (the Tibetans). Using theodolites located 150 miles away from his target, and laboring and crunching data, and using no small amount of trigonometry, Sikdar finally announced, in 1852, not only the height of this peak, but also that it had the highest elevation above sea level: 29,002 feet.

Here’s the thing, though. After all the measurements and number crunching and double-checking, what Sikdar really came up with was 29,000 feet exactly. Well, he must have thought, no one is going to believe that. So to avoid the illusion that he just merely came up with a rounded guesstimate, he added an arbitrary two feet. So, at the beginning, when I (or Stephen Fry) asked, who was the first person to put two feet on top of Mount Everest? Yep: Radhanath Sikdar.

Over the years, the elevation of the mountain has been refined and its official height now is 29,029 feet. (It’s those last 10 yards that’ll get you.)

Sikdar was soon appointed Superintendent of the Meteorological Office and revolutionized weather forecasting. He died in 1870, and in 2004, an Indian postage stamp was issued in his honor. Sikdar is considered the “first scientist of modern India.”

One sticky wicket that remained was what to actually call the mountain, since it had a variety of local names. In 1865, Waugh decided to solve the problem by naming it after his predecessor as Surveyor General of India, George Everest. Everest objected, to no avail, claiming that his name could not be written in Hindi or pronounced by the local peoples. Or even by English-speaking folk, it would seem. While we pronounce the mountain “Eh-verest,” old George actually pronounced his name with a long e, “Ee-verest.”

“Mount Sikdar” would have been far more appropriate.

 

Resources:

Soutik Biswas, “The man who ‘discovered’ Everest,” BBC News Online, October 20, 2003, http://news.bbc.co.uk/2/hi/south_asia/3193576.stm.

Utpal Mukhopadhyay, “Radhanath Sikdar: First Scientist Of Modern India,” Science and Culture, May–June, 2014, http://www.scienceandculture-isna.org/may-june-2014/05%20Art_Radhanath%20Sikdar%20First%20Scientist…by_Utpal%20Mukhopadhyay_Pg.142.pdf.

“Mount Everest,” Q.I., http://qi.com/infocloud/mount-everest.

“Barthomeaus Pitiscus,” Wikipedia, last modified on May 2, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Bartholomaeus_Pitiscus.

“Decimal Mark,” Wikipedia, last modified on December 27, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Decimal_mark.

“Great Trigonometrical Survey,” Wikipedia, last modified November 22, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Great_Trigonometrical_Survey.

“History of Trigonometry,” Wikipedia, last modified on December 4, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/History_of_trigonometry.

“John Napier,” Wikipedia, last modified on January 1, 2016, retrieved January 4, 2016, https://en.wikipedia.org/wiki/John_Napier.

“Mount Everest,” Wikipedia, last modified on December 30, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Mount_Everest.

“Radhanath Sikdar,” Wikipedia, last modified on December 28, 2015, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Radhanath_Sikdar.

“Trigonometry,” Wikipedia, last modified on January 4, 2016, retrieved January 4, 2016, https://en.wikipedia.org/wiki/Trigonometry#Overview.

 

 

Share this post