MATH AT WAR In June 1942 Japanese naval commanders saw a chance to destroy the US Navy in the Pacific Ocean Six months earlier the Japanese had attacked the US fleet at Pearl Harbor Japan planned to draw the remaining US ships into a trap The Japanese would launch a surprise attack at Midway Island But they did not know that the Americans were waiting for them US experts had cracked Japan's secret naval codes and knew the attack at Midway was coming An American torpedo On June 4 the United States attacked the bomber climbs away from a burning Japanese In the three day battle they sank Japanese ship during four Japanese aircraft carriers The Japanese the Battle of Midway navy never recovered from defeat the
American code breakers were mathematicians who changed the course of warfare Armies have always used codes to keep their plans secret from the enemy and the enemy has always tried to break those codes Mathematics is the basis of modern code breaking George Cayley's principles of flight led to the first powered flight by the Wright Brothers at Kitty Hawk North Carolina in 1903 RANGE OF USES Math has also had many other uses in military history Geometry or the study of shapes was the basis of navigation at sea Surveyors used geometry to map unknown territory With the development of artillery mathematics allowed gunners to figure out the range of targets In the late eighteenth century George Cayley used math to figure out the principles of flight In the late twentieth century math became the basis for all computers Computers became widely used in weaponry And military computers are likely to dramatically change warfare in the future as well 5
NAVIGATION Navigation is the science of planning and following a route For centuries sailors had no way to chart their course other than to use math to figure out their location Tn the third century BCE the Greek mathematician Eratosthenes had the idea of placing an imaginary grid around the Earth The grid had lines running from north to south and from east to west In around 120 BCE a Greek astronomer named Hipparchus used math to plot locations on these lines He used a method modern mathematicians call triangulation Early ships like this Phoenician galley usually stayed close to shore so sailors Could navigate by using landmarks on coast the
SCIENCE FILE Triangulation is based on the idea that someone who knows the length and angles of one side of a triangle can figure out the length of the other two sides ooooo FILE MEASURING LATITUDE A position north or south on Earth is called latitude A position from east to west is called longitude Sailors found their latitude by measuring the angle of the sun or stars above the horizon They then used a version of triangulation to figure out their position on the globe Sailors measured the angle of the sun or stars in degrees of elevation The first sailors held out their arms and used their fingers as a rough measure In the ninth century Arabian navigators invented a device called a kamal The kamal used knots in a string to measure angles Dead Reckoning Before it was possible to measure longitude sailors used dead reckoning to calculate their position This method was based on the ship's last known position called a fix The sailors used their speed direction and how long they had been sailing to figure out their new position If one fix was wrong however later fixes became even more inaccurate On a long voyage sailors might think they were hundreds of miles from their true position oooooooooooooooooo The kamal was a piece of wood with a knotted string One of the knots was held in the teeth and the kamal was held out at arm's length Matching up the edges of the board with a known star and the horizon gave the sailor latitude his
