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# Celebrating Jean-Félix Picard's Birthday With Geodetic Trivia

If you find having a favourite map projection a delightfully geeky quirk, you're going to want to raise a toast in honour of Jean-Félix Picard. Geodetics and cartography owe a debt of gratitude to the 17th century scientist who made the first accurate measurement of the Earth's size.

Jean-Félix Picard was born on this day in 1620 in La Flèche, France. He's worth celebrating because in 1671, he published Mesure de la Terre, one of the first accurate measurements of the Earth's size. He managed to measure the size of the Earth to within fractions of our current best-estimates using triangulation, mathematics, and a whole lot of patience.

Using triangulation to measure the width of a river in the 16th century. Source: Hulsius

Picard's not-so-secret technique was blending the precision of measuring distances with triangulation and the mathematical wizardry of algebra and geometry.

He started by very carefully measuring the arc length of a single degree in latitude with excruciating precision with thirteen triangles along the meridian between Paris and a clock tower in Amien. He dropped that into the relationship between radius and arc length for circles, jiggling around measured arc length and the subtended angle to extract the radius of our planet.

Here's the crazy bit: he measured the arc length of 1 degree latitude as 110.46 kilometers, thus calculated the terrestrial radius of 6,328.9 kilometers. Our current best measurement of the polar radius* is 6,356.7 kilometers. That's 0.44% error, otherwise known as "Impressive."

Like all scientists, Picard built on the work of those who came before**. Francesco Maurolico published the basic sketch of methodology in his Cosmographia in 1543, while Willebrord Snellius made the first applied attempt by measuring out the distance between a pair of Dutch towns separated by a degree latitude in 1615. He published his results in Eratosthenes Batavus two years later, listing the arc length as 107.395 kilometers. While his technique was sound, Picard's meticulous accuracy when following the same methodology made the difference between "pretty good" and "astonishing."

Tip via Physics Today's Facebook feed.

* Polar radius matches up with the radius for an arc segment subtended by latitude. You might be more familiar with the equatorial radius, which is the radius for an arc segment subtended by longitude, as that's how we typically compare the Earth to exoplanets.

** Update: Quite a few comments are grumbling that "X did it first!" Yes, Erastothenes came up with a neat technique, but lacked the accuracy. More fascinatingly, Abu Arrayhan Muhammad ibn Ahmad al-Biruni developed a new technique that produced somewhere between 0.33 and 0.67% error. Picard was impressive for doing the boring, methodical, meticulous work to get really good numbers to plug in, thus getting a genuinely accurate number out.

### DISCUSSION

Abu Arrayhan Muhammad ibn Ahmad al-Biruni calculated the radius with 0.26 % error at the end of the 10th century. So he was more accurate and earlier, but I guess not European so he doesn't count, am I right ppl.