to Chinese, Indian, and Mesopotamian mathematicians,
and helped build the great pyramids of Egypt.
For any right triangle,
the square of the hypotenuse is
the sum of the squares of the other two sides.
But Pythagoras could have been
the first person to offer a proof of it,
rearranging in a square four copies of the triangle.
Thales’ theorem
A circle’s diameter
and the chords from its end points
to a common point on the circle
construct a right triangle.
Ancient trigonometry
derived from the chord function.
The chord of an angle between two radii
times the radius of the circle is the distance
between the two points on the circle.
The chord of 60° is the radius.
The sum of the squares
of the chords of supplementary angles
(whose sum is 180°)
is the square of the diameter.
Irrational triples
Infinitely many
sets of three
whole numbers
satisfy
the Pythagorean theorem
and many more
are not even rational.
The X and Y axes in the Cartesian coordinate system form right angles,
and the line between the origin and any point not on either X or Y axis is the hypotenuse of a right triangle.
The sine and cosine in modern trigonometry are ratios of the hypotenuse with the opposite
and adjacent sides of a right triangle whose hypotenuse starts at the origin of the X and Y axes
and ends at the circumference of the unit circle whose center is the origin.
The Greek root of the word trigonometry is trigōnon,
an ancient triangular lyre or harp.
The vibration of musical strings create standing waves
and their form can be expressed using trigonometric functions.
Fibonacci’s method for generating Pythagorean triples
seems to me to be complete. If you are interested, I can give you
a Java program that implements his method.
The X and Y axes in the Cartesian coordinate system form right angles, and the line between the origin and any point not on either X or Y axis is the hypotenuse of a right triangle. The sine and cosine in modern trigonometry are ratios of the hypotenuse with the opposite and adjacent sides of a right triangle whose hypotenuse starts at the origin of the X and Y axes and ends at the circumference of the unit circle whose center is the origin. The Greek root of the word trigonometry is trigōnon, an ancient triangular lyre or harp. The vibration of musical strings create standing waves and their form can be expressed using trigonometric functions.
Fibonacci’s method for generating Pythagorean triples seems to me to be complete. If you are interested, I can give you a Java program that implements his method.
See also in The book of science:
Readings on wikipedia:
Other readings: