Trig Nature

7/30/2019 Trig Nature

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Trigonometry- derived from

the words trigonon which

means triangle and

metron which means to

measure. A branch of mathematics

concerned with the

relationship between angles

and their sides and the

calculations based on them.


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Trigonometry was first

invented by the Greeks,

and was used for

navigation and astronomy.

It was first used by Hipparchus

in 150 BC. He started out withcreating a bunch of tablets with

certain ratios. He then went on to start to define chord, sine,

and cosine. Claudius Ptolemy continued Hipparchus work,

and improved on his tables. He was also able to figure out how

to calculate square roots. He then continued to work on Sine

and Cosine rules, and defined for us the inverse functions of Sine

and Cosine. Also during the 10th and 11th centuries in

Egypt, mathematicians were able to determine other formulas.


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During Medieval times,

the Chinese developed the tangent

function, and the Indians created sine

and cosine tables. They also helped todevelop the formal definitions for

cosine, cotangent, secant, and

cosecant.

In 1559, Bartholemaeus

Pitiscus published a workcalled Trigonometry, which

is probably where we get the

name today.


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Pitiscus

Hipparchus

Aryabhata

Regiomonatus

Guo Shoujing

Theodosius


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Although Pitiscus worked much in the

theological field, his proper abilities concerned

mathematics, and particularly trigonometry.

The word 'trigonometry' is due to Pitiscus and first

occurs in the title of his work Trigonometria: sive desolutione triangulorum tractatus brevis et

perspicuus first published in Heidelberg in 1595 as

the final section of A Scultetus's Sphaericorum libri

tres methodice conscripti et utilibus scholiis expositi.

The first section, divided into five books, coversplane and spherical trigonometry.

In the first book he introduced the main definitions

and theorems of plane and spherical trigonometry.

The third of the five books is devoted to plane

trigonometry and it consists of six fundamentaltheorems.

The fourth book consists of four fundamental

theorems on spherical trigonometry, while the fifth

book proves a number of propositions on the

trigonometric functions.

Trigonometry: or, the doctrine of triangles.


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He made an early contribution to

trigonometry producing a table of chords,

an early example of a trigonometric

table; indeed some historians go so far as

to say that trigonometry was invented byhim.

Finally let us examine the contributions

which Hipparchus made to

trigonometry.

Even if he did not invent it, Hipparchus is

the first person whose systematic use of

trigonometry we have documentary

evidence.

If this is so, Hipparchus was not only the

founder of trigonometry but also the

man who transformed Greek astronomy

from a purely theoretical into a practical

predictive science.


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The mathematical part of the

Aryabhatiya covers arithmetic,

algebra, plane trigonometry

and spherical trigonometry.

We now look at the

trigonometry contained in

Aryabhata's treatise.

He also introduced the versine(versin = 1 - cosine) into

trigonometry.


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Regiomontanus made important

contributions to trigonometry and

astronomy.

In the Epitome Regiomontanus, realising

the need for a systematic account of

trigonometry to support astronomy,

promised to write such a treatise.

With Book II the study of trigonometry

gets under way in earnest.

Books III, IV and V treat spherical

trigonometry which, of course, is of major

importance in astronomy.


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Making sense of the data gathered from the

instruments required a knowledge of

spherical trigonometry and Guo devised

some remarkable formulae.

We should now look at the rather remarkable

work which Guo did on sphericaltrigonometry and solving equations.

The first column is the value of x using Guo's

formula taking an accurate modern

approximation to , the second column is the

result given by the formula with = 3, while

the third column is the correct answer

calculated using trigonometry (in fact the

cosine).


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Sphaerics contains no trigonometry

although it is likely that Hipparchusintroduced spherical trigonometry

before Sphaerics was written

(although, one has to assume, after

the book on which Sphaerics is based,which would certainly be the case if

this earlier book was written by

Eudoxus).

Perhaps it is worth remarking that

despite our comment above that the

work contains no trigonometry, there

are some results which we could easily

interpret in trigonometrical terms.


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Astronomy has been studied formillennia by civilizations in all

regions of the world. In our modern age, being able

to apply Astronomy helps us tocalculate distances betweenstars and learn more about the

universe. Astronomers use the method of

parallax, or the movement ofthe star against the backgroundas we orbit the Sun, to discover

new information about galaxies. Menelaus Theorem helps

astronomers gather informationby providing a back drop inspherical triangle calculation.


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Trigonometry is used in geology to

estimate the true dip of beddingangles. Calculating the true dip

allows geologists to determine the

slope stability.

Although not often regarded asan integral profession, geologists

contribute to the safety of many

building foundations.

Any adverse bedding conditionscan result in slope failure and the

entire collapse of a structure.


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http://www.hackingtheuniverse.com/science/histo

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technology/genarticles/timeline-of-trigonometry

http://www.clarku.edu/~djoyce/trig/apps.html

http://www.edurite.com/kbase/examples-of-

trigonometry-in-nature
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