Born in 1580 in

the Netherlands, Willebrord van Roijen Snell was the son of a

linguist and

mathematician. From a family of means, he was predetermined to become a

lawyer, but his own interests led him elsewhere. With a fascination for

mathematics and ingrained talent, he dual-tasked studying

law and lecturing on mathematics at the age of eleven at

Leyden University. His law studies continued in

Paris from 1600 to 1604, but returned to Leyden University afterwards to take up

mathematics and other sciences full time. He became a full

professor of

astronomy and

mathematics by 1613, following in the footsteps of his father, and continued his studies up to his death in 1626.

Snell is well-known for three significant discoveries. His first was an accurate calcuation of the circumference of the earth through triangulation between first three landmarks in Leyden, and then between Leyden, Alkaar, and Bergen-op-Zoom. He found the number 38,500km, which was surprisingly close to the actual number, ~40,000km. The techniques he devised founded the modern field of mapmaking.

His second major acheivement was a newly accurate calculation of the number pi, up to 34 decimal places. He published this calculation in the paper Cyclometricus in 1621. He used an extremely difficult method, as logarithm had not yet been fully developed, relying on the imagination of a polyhedron with 1,073,741,824 sides. Yikes! This 34 decimal place approximation of pi is now known as Snell's number in his honor (although Van Ceulen had used the same method to find a 35 decimal approximation before Snell, he never published. You snooze, you lose.)

Snell is most famous, however, for his studies in optics. In 1613, he found that the path of a light ray described by the ancient Greek mathematician Ptolemy:

*θ*_{1} *θ*_{2}
-- = --
*v*_{1} *v*_{2}

..where θ 1 and 2 represent the angles of observation, and

*v* 1 and 2 represent the velocities in the respective media, was actually incorrect. He devised a new method of calculating the path, now called

Snell's Law (a more general, applicable form of Snell's Law can be found under that write-up), which goes as follows:

sin*θ*_{1} sin*θ*_{2}
----- = -----
*v*_{1} *v*_{2}

It more accurately described the refraction of a beam of light than Ptolomy's equation had done, and is still used today. Light refraction comes into play when a beam of light crosses from one

media to another. For example, have you ever stuck a

pencil into a glass of water? Did you notice how it looked bent, even though it became perfectly straight again when you pulled the pencil out? This is because of Snell's Law. The light slows down in the denser water, and thus the angle of observation must change to keep the ratio equal.

These three major discoveries have placed Willebrord van Roijen Snell firmly in the history books as one of the great European mathematicians.

Sources: *BBC History, Willebrord van Roijen Snell, http://www.bbc.co.uk/history/historic_figures/snell_willebrord_van_roijen.shtml

*Anton, Howard, Calculus: A New Horizon. 6th ed. New York: John Wiley & Sons, Inc.

Professor_Pi has kindly informed me that his name is often

Latinized to

Snellius. This would make sense, taking into consideration that is epochal work Cyclometricus was written in Latin.