Transcript Melanie Vogelx

Trigonometry
By Melanie
What is trigonometry?
Trigonometry is defined as “a branch of mathematics dealing with the
relations of the sides and angles of triangles and with the relevant
functions of an angles”
What does this mean?
Trigonometry uses the Greek words “trigon” and “metron” to make up
its name
Meaning “triangle” and “a measure”
Trigonometry means the measuring of angles and sides of triangles
What makes trigonometry interesting?
Who doesn’t like triangles!!
Ever want to figure out how tall a mountain is?
Want to calculate the distance to the sun?
Trigonometry has got your back!
How do triangles affect my life?
How else do I cut my pizza evenly?
But really…
Trigonometry is used in our every day life.
Its used to build our homes, our vehicles, our TV's, and almost every
piece of technology we own. Trigonometry was used to help make even
our music. Knowledge about sound waves has come from
trigonometry equations!
Euclidean’s geometry (Don’t worry, this is
relevant)
Euclid was a Greek mathematician
The sum of the angles in a triangle always equals to two right angles
In Euclid’s geometry the three sides of a triangle add up to a straight line
But this has limitations,
Hipparchus
A Greek astronomer and mathematician named Hipparchus studied the
movements of the Earth and the Sun to answer the problem:
» Does the sun revolve around the Earth or does the Earth revolve around
the Sun?
Using Euclid’s geometry, Hipparchus tried to find an answer to this question
but realized that Euclid’s geometry wasn’t made for the comparison of
moving things
Hipparchus used the Pythagorean theorem to calculate a list of sines and
cosines to then be able to measure the changes in triangles
Pythagorean theorem
Pythagoras wanted to prove A2 + B2= C2
Two thousand years earlier the Sumerians
already knew about this equation and used it
in many of their measurements but
Pythagoras wanted to be sure it was always
going to be true.
Pythagoras stated that in any right triangle,
the area of the hypotenuse square is equal to
the sum of the areas of the adjacent and the
opposite squares.
Think triangles are boring?
Try this!
• Draw a straight line on a piece of paper
• Draw more lines starting from the middle of your first line that are
half the size of the diameter and going in any direction
• Keep your pencil on the paper
• Then make a straight line from where your pencil ended and connect
it to your first line making a 90 degree angle.
• This will make a triangle! Do this a few times
It will look something like this!
What do you notice?
If you continued to draw triangles like this until they are all side by side, it
will create a circle!
Many mathematicians have found that they can relate this to a repeating
wave, called sine waves.
These waves are commonly found in nature
Let’s wrap this up…
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Triangles are awesome
They help build things we use
We rely on triangles to cut our pizzas evenly
Its fun to draw
It can relate to sine waves
Hipparchus is one smart cookie
Bibliography
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http://scienceforkids.kidipede.com/math/trigonometry/
http://www.cut-the-knot.org/WhatIs/WhatIsTrigonometry.shtml
http://www.historyforkids.org/learn/greeks/science/astronomy/hipparchus.htm
http://www.mathsisfun.com/flash.php?path=/geometry/images/circletriangle.swf&w=405&h=510&col=#FFFFFF&title=Sine,+Cosine,+Tangent
http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
http://en.wikipedia.org/wiki/Euclidean_geometry
http://www.ducksters.com/kidsmath/pythagorean_theorem.php
http://answers.yahoo.com/question/index?qid=20080427182220AAyGhQr