In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation”.
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i^2 = −1. The square of an imaginary number bi is –b^2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary. Originally coined in the 17th century as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler and Carl Friedrich Gauss.
About 1600, Galileo performed his famous inclined plane experiments and discovered that the acceleration of a freely-falling object is constant - that is, the object's acceleration does not change while the object is in free fall. The acceleration of a freely-falling object - any freely-falling object - near the surface of the Earth is about sqrt(19.6x) meters per second.