Many scholars contributed to inventing trigonometry
You wanted to know
"Who is the person that discovered trigonometry?" asked a young Schaumburg Township District Library patron who attended the "Summer Scientists" program.
Wanting to determine distances between stars, across land and sea, ancient Greeks developed trigonometry - triangle measure.
Before 100 B.C., scholars including Hipparchus and later Ptolemy and Menelaus contributed to the mathematical invention. Hipparchus initiated the use of chords, a key component of trigonometry, to measure angles within a circle. Ptolemy, using older Babylonian strategies, refined the chord concept.
By A.D. 1000, Arab and Indian mathematicians improved Greek trigonometry calculation methods.
The general trigonometry concept of the relationships between lengths of triangle sides and angle measurements dates to even earlier times. Ancient Egyptians created formulas to determine the slope of an incline for use in constructing pyramids.
The Rhind Mathematical Papyrus, written by an Egyptian scribe in 1650 B.C. and accessible online at the British Museum website, includes a kind of math quiz with problems and solutions for determining triangle measurements. This math how-to is a copy of an older papyrus that dated to 1800 B.C.
"Trigonometry is, of course, very old, and no single person could be said to have discovered it. It is a subject with many applications in the sciences and engineering." said Lynn Narasimhan, director and professor of the college of Science and Health at DePaul University,
Trigonometry uses ratios called sine, cosine, tangent, cotangent, secant, and cosecant to determine the length of unknown triangle sides or angle degrees within a triangle.
Prior knowledge of algebra and geometry is needed before applying trigonometry calculations. Generally called trig, it is usually taught in the junior year of high school and is sometimes called Algebra 3 or Advanced Algebra/Trig.
Students will be familiar with the mnemonic SOHCAHTOA, which explains trig formulas - sine opposite hypotenuse, cosine adjacent hypotenuse and tangent opposite adjacent - the formulas needed to solve the side/angle relationships of right triangles.
Narasimhan suggests Clark University's "Dave's Short Trig Course" website for specific information about trigonometry.
The site connects the use of trigonometry calculations for problem solving in the fields of chemistry, physics, architecture, construction, surveying and engineering, and in math for solving problems in calculus, linear algebra and statistics. Methods for solving trig problems and examples are included on the site.
Architects use sine to determine distances, such as the height of a wall, and tangent to calculate wall length. Mechanical and chemical engineers use cosine and sine to determine displacement. Aerospace engineers apply sine when calculating wind corrections to keep airplanes on track.
Civil engineers use trig functions, including sine, cosine and tangent, to determine the structural integrity of a building and to figure out how wind, water and other weather conditions will affect the new construction. They determine height, width and angles needed when designing buildings, bridges, dams and other projects.
Sine, cosine and tangent are used in physics to calculate velocity and angles, for instance, to determine the angle of a rope dangling from the top of a building. Electrical engineers might use secant to determine electrical interactions.
Check it out
The Schaumburg Township District Library suggests this title on geometry:
• "Euclid: The Great Geometer" by Chris Hayhurst