History of Mathematics and Current Application
should have a 1. A topic 2. Create a written narrative of the topic, include significant contributions from cultures and individuals. 3. Describe important current applications of the topic that would be of particular interest for students
Number systems
Algebra
Geometry
calculus
Discrete Mathematics
Probability/Statistics
Measurement
Example: Triginometry
Topic: Trig Tables
Written Narrative: The roots of trigonometry come from the study of astronomy and a desire to understand the placement and movement of the stars.
The first known table was created by a Greek astronomer and mathematician named Hipparchus (190-120 BC). This table was based on the relationship between chords and angles. (Smoller, 2001)
Ptolemy (100-178 AD) expanded the work to develop one of the most famous trig tables that contained values for all angles up to 180 degrees. Understanding the Pythagorean Theorem as well as formulas for angles and angle addition allowed mathematicians to build on the values from constructed angles to expand the values of trig tables. (Joyce, 1996)
Babylonian, Greek and Indian developments mingled to create the more modern form of trigonometry, including the use of the term sine. The ideas of tangent and cotangent developed based on the lengths of cast shadows. The functions of secant and cosecant were later derived based on tables used for navigation. (Smoller, 2001)
In the 17th century mathematicians such as Newton developed power series for trig functions allowing for tedious but accurate calculations. (Joyce, 1996)
Computers and scientific calculators now make these previously complicated procedures so easy that most people do not understand the complicated history that was required to develop these values.
Current Application: Trigonometric functions are currently used all around us. They play a role in navigation for boats, planes and satellites. They are also crucial in surveying and engineering. They ensure the structural integrity of bridges as well as skyscrapers.
