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Crashing Trigonometry Heads ON!
Trying to figure it out myself...
Going back to 150 B.C.
and we find Hipparchus on RODHES ISLAND, OFF TURKEY, UNDER GREEK PROTECTORATE, 2,200 YRS AGO.
Wanted to know why you Sir made this subject so hard for our kids?
Was not really my intention to make it look so hard. Actually my friend... It was invented for my own use as an avid Astronomer, astrologer and geographer. My knowledge of math and proportions and ratios gave me a head start...Ptolemy improved it in his 'Almagest'... and I feel so sorry for enforcing our Geocentric model on Copernicus and Galileo! Our mistake!
Luckily we understand each other Sir. But the name trigonometry sometimes is too cumbersome...
Is a composite word for my time which was written in Hellenistic Greece like this:τριγωνομετρία. Wow, this translator of yours really catches and keeps up with what I really want to say... trigo is 'trig onus' which roughly means triangle or three angles, and metro from metron, measurement.
That makes it a little clearer now... The cloud is going away in our minds.
Why don't we explain together this subject to your kids? Two minds think better...
There you go...lets see..hum!
When Hipparchus was a kid in Nicaea(Today Turkey), he used to wonder how things were moving around him, but at nights there was no light...so He gazed into the stars. The easier game for him was to get sticks and tied them with chords.
So his mind was used to see the shadows of the sun on this rudimentary triangle shaped with 3 sharpened woods. When he got older he carried that ability into the diagrams and elliptical shapes.
He studied cosmography and astrology, inherited from Babylonians and Chaldean. His math was strong and wanted to figure out the universe himself. Eventually he came up with trigonometry to help him calculate distances from the sun and the moon to our planet. His first invention was the astrolabe that helped Columbus to make it to Caribbean shores. But lets cut on history and go to the basics.
IF YOU HAVE A TRIANGLE YOU HAVE TO REALIZE THIS:
NO MATTER HOW BIG THE TRIANGLE IS...
AN HYPOTENUSE AND ITS RESPECTIVE ADJACENT AND OPPOSITE SIZES WIL 'LOCK IN' A CONSTANT VARIABLE or ratio...
intrinsically relating angles and the measurements of chords and sides
THANKS TO PYTAGORAS WE KNOW THAT
WHAT HIPPARCUS DID WAS TO CREATE NAMES FOR DIFFERENT RATIOS OF THAT TRIANGLE...SO HE CALLED THE PROPORTION BETWEEN..RED 'Y' AND BLUE 'R' SINUS
WHERE @ IS the particular angle for this unique triangle
Consequently Hipparchus gave the other names to similar combinations as is explained down in a MORE ANALITHICAL GRAPH. Sorry kids...trying to break it down as much as I can, but you will have to memorize somehow what is tan, cos or sin. Same as studying multiplication tables... AGAIN SORRY!
Surprisingly Egyptians adopted trigonometry using ancient Mnemonics
TAN(@)= OPPOSITE/ ADJACENT
We suspect that Isis 'per se' was close to their son Horus, unless in hieroglyphic language Isis=Ad
We can soak up again your brain with the numbers 3,4 and 5...as shown on the graph the relationship is unique and according to Pythagoras 3 and 4 will give you always an Hypotenuse value of 5( FOR ANGLES OF 37, 53 AND 90 DEGREES AS TAUGHT BY TEACHERS)
IF YOU INCREASE TO 6 AND 8 YOU WILL GET AN HYPOTENUSE OF 10 AND SO ON..
in another hub we will work with functions and identities.