Choose three (3) of the topics below , do a little research to find out more abo
ID: 3035855 • Letter: C
Question
Choose three (3) of the topics below, do a little research to find out more about them, and write a 4-8 sentence summary in your own words about EACH of the three topics. You must cite your sources. (Include the source in some reasonable way, but it doesn’t have to be an official citation format.)
Who invented the logarithm and why?
Where does the word ‘algebra’ come from?
What was the first algebra word problem ever written?
Rene Descartes and Cartesian coordinates.
Where and when was trigonometry first used?
Who invented the exponential notation?
Explanation / Answer
Who invented the logarithm and why?
Answer-
Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. The objective of both men was to simplify mathematical calculations. Napier's approach was algebraic and Burgi's approach was geometric. Neither men had a concept of a logarithmic base. Napier defined logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents. The possibility of defining logarithms as exponents was recognized by John Wallis in 1685 and by Johann Bernoulli in 1694. The invention of the common system of logarithms is due to the combined effort of Napier and Henry Briggs in 1624. Logarithms are useful in many fields from finance to astronomy. Moreover, because the logarithmic function log(x) grows very slowly for large x, logarithmic scales are used to compress large-scale scientific data.
Where does the word 'algebra' come from?
Answer-
The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi.The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabr was to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation. In fact, the title has been translated to mean "science of restoration (or reunion) and opposition" or "science of transposition and cancellation" and "The Book of Completion and Cancellation" or "The Book of Restoration and Balancing."Jabr is used in the step where x - 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is "restored" or "completed" back to x in the second equation.Muqabalah takes us from x + y = y + 7 to x = 7 by "cancelling" or "balancing" the two sides of the equation.Eventually the muqabalah was left behind, and this type of math became known as algebra in many languages.
When and where was trigonometry first used?
Answer-
The complex origins of trigonometry are embedded in the history of the simple word "sine," a mistranslation of an Arabic transliteration of a Sanskrit mathematical term! The complex etymology of "sine" reveals trigonometry's roots in Babylonian, Greek, Hellenistic, Indian, and Arabic mathematics and astronomy.Its origins lie in the world of astronomy and spherical triangles. Before the sixteenth century, astronomy was based on the notion that the earth stood at the center of a series of nested spheres. To calculate the positions of stars or planets, one needed to use concepts we now refer to as trigonometry.
The earliest uses of trigonometric functions were related to the chords of a circle, and the recognition that the length of the chord subtended by a given angle x was (in modern terms) 2sin(x/2). The Greek astronomer and mathematician Hipparchus produced the first known table of chords in 140 BC. His work was further developed by astronomers Menelaus (ca. AD 100) and Ptolemy (ca. AD 100), who relied on Babylonian observations and traditions.Babylonian and Greek influences mingled with rich native mathematical developments in India around AD 500 to produce a trigonometry closer to its modern form.