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Trigonometry - Moments in History
- Stella
- Sep 9, 2024
- 4 min read
Updated: Jan 2
Below you will find some examples of how useful Trig has been in history.
Egyptian pyramid building - Using Trig for Construction
Khufu’s pyramid is perhaps the most colossal single building ever erected on the planet. Its sides rise at an angle of 51°52′ and are accurately oriented to the four cardinal points of the compass. The Great Pyramid’s core is made of yellowish limestone blocks, the outer casing (now almost completely gone) and the inner passages are of finer light-coloured limestone. The interior burial chamber is built of huge blocks of granite. Approximately 2.3 million blocks of stone were cut, transported, and assembled to create the 5.75-million-ton structure, which is a masterpiece of technical skill and engineering ability.
The ancient Egyptians built pyramids primarily as tombs for their pharaohs and important figures. They believed in an afterlife where the pharaohs would continue to rule, so the pyramids served as eternal resting places. The structures were filled with treasures, food, and other items necessary for the afterlife. Pyramids symbolised the rays of the sun, and their shape was meant to help the soul of the pharaoh ascend to the heavens.
Great Pyramid's Precision: The Great Pyramid of Giza was originally 146.6 meters tall and is aligned almost perfectly with the cardinal points—north, south, east, and west.
Oldest of the Seven Wonders: The Great Pyramid is the oldest of the Seven Wonders of the Ancient World and the only one still largely intact.
Construction: Built around 4,500 years ago, it is believed to have taken 20 years and around 2.3 million stone blocks, each weighing 2.5-15 tons.
Not Built by Slaves: Contrary to popular belief, it’s now thought that skilled labourers, not slaves, built the pyramids. Workers were housed in nearby villages and likely well-compensated.
Chambers and Mysteries: Inside the Great Pyramid are multiple chambers, including the King’s and Queen’s chambers. Many mysteries still surround its construction techniques and purpose.
Construction
The Egyptians used a mix of observation, practical knowledge, and early mathematical concepts to build the pyramids. Their understanding of geometry and measurement was advanced. They likely used simple tools like ropes and plumb bobs for alignment and leveling. The seked, an ancient unit of slope, helped them calculate the angles of the pyramid sides. By carefully measuring the base and using astronomical alignments (such as aligning with the cardinal points), they achieved precise results.
Ramp Theories: Several theories explain how the massive stones were lifted, with the most popular suggesting long straight or spiral ramps built around the pyramid.
Limestone Casing: The pyramids were originally covered in smooth white limestone casing stones, giving them a shiny, polished appearance.
Labor Organization: Workers were organized into highly skilled teams, with evidence of specialized roles like quarrying, transporting, and stone setting.
Transportation of Stones: Stones were likely transported using sledges over wetted sand, reducing friction.
The sinking of the Luscitania - Using trig for firing torpedos
The sinking of the Lusitania on May 7, 1915, was a major event during World War I. A British ocean liner, it was torpedoed by a German U-boat submarine off the coast of Ireland, leading to the deaths of 1,198 people, including 128 Americans.
Germany had warned that ships entering British waters could be targeted due to the ongoing war. Despite these warnings, Lusitania continued its voyage from New York to Liverpool. The attack caused a significant diplomatic rift between Germany and neutral countries like the United States, contributing to shifting public opinion toward involvement in the war. The sinking is considered one of the key factors leading to the U.S. joining World War I in 1917
The RMS Lusitania was located about 11 miles off the southern coast of Ireland near the Old Head of Kinsale when it was struck. The German U-boat, U-20, commanded by Kapitänleutnant Walther Schwieger, was patrolling the area off the southern Irish coast. Schwieger spotted the Lusitania and fired a torpedo at the ship, which struck on the starboard side, leading to its rapid sinking
U-20 surfaced again at 12:45 as visibility was now excellent. At 13:20, something was sighted and Schwieger was summoned to the conning tower: at first it appeared to be several ships because of the number of funnels and masts, but this resolved into one large steamer appearing over the horizon. At 13:25, the submarine submerged to periscope depth of 11 metres and set a course to intercept the liner at her maximum submerged speed of 9 knots. When the ships had closed to 2 nautical miles (3.7 km) Lusitania turned away, Schwieger feared he had lost his target, but she turned again, this time onto a near ideal course to bring her into position for an attack. At 14:10, with the target at 700 m range he ordered one gyroscopic torpedo to be fired, set to run at a depth of three metres
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