Columbus Day – The Mathematics of Navigation

Columbus sailed west using dead reckoning: course and distance estimated by log and compass. He did not know celestial navigation well, which is why he miscalculated the circumference of the Earth. True longitude determination required accurate clocks (Harrison’s chronometer, 1761) or lunar distances (the method of lunars). Spherical trigonometry (law of cosines for sides) is essential: cos(a) = sin(δ) sin(φ) + cos(δ) cos(φ) cos(HA). Columbus’s voyage was a mathematical failure but a geographical success. Navigation is applied geometry.