Math Applications

Archimedes was a mathematician, physicist, astronomer, engineer, inventor, and weapons designer. He was the most-famous mathematician and inventor in ancient Greece. He was born in the Greek city-state of Syracuse on the island of Sicily in approximately 287 BC. 

He is known for his formulation of a hydrostatic principle (known as Archimedes’ principle) with which he could prove whether the king’s gold crown had silver in it.  The story goes that the king wanted to find out if his crown was made of pure solid gold or if it was filled with other metal.

Archimedes is credited with finding the value of pi to two decimal places (3.14) in 250 BC.

Archimedes Contributions to Science and Math

Among his many contributions to science and mathematics, some are:

• He invented the science of mechanics and hydrostatics.

• Discovered the laws of levers and pulleys, which allow us to pull heavy objects using small forces. 
• Invented the most fundamental concept of physics known as center of gravity.
• Archimedes’ especially important discovery was of the relation between the surface and the volume of a sphere. Surface Area = 4* π * R**2 and Volume = (4/3)* π * R**3
• In mathematics, Archimedes showed how exponents could be used to write bigger numbers. He proved that to multiply numbers written as exponents, the exponents can be added together to get the multiplication result.

Euclid

Euclid was a Greek mathematician, often referred to as the ‘father of Geometry’. He spent most of his time in Alexandria, Egypt during the years 323 – 283 BC.

His treatise Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19^th or early 20^th century.

In the Elements, Euclid deduced the theorems of what is now called Euclidean Geometry. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigor.

Pascal

As the Fibonacci numbers increase in magnitude, the ratio between succeeding numbers approached the number called the golden ratio, whose value is 1.6180…, or (1 + √5)2.  Fibonacci sequence numbers are said to have a golden ratio.  

Two quantities are in the golden ratio if the ratio of the larger number to the smaller number is the same as the ratio of their sum to the larger number a/b = (a + b)/a, where a is the larger number. The golden ratio (symbol Greek letter “phi” φ) is a special number approximately equal to 1.618. 

The number phi is a mathematical concept that people have known about since the time of the ancient Greeks. It is an irrational number like the mathematical constants pi and Euler’s number ‘e’, meaning that its terms go on forever after the decimal point without repeating. 

Scientists discovered such Fibonacci sequences in nature – in the spirals of sunflower heads, the arrangement of pine cone’s bracts, in the spiral in snail shells, in the tree arrangement of leaves on the stem.

Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, also known as Fibonacci.  Fibonacci was born in the year 1170 in Italy and was educated in North Africa. He wrote Liber abaci in 1202; “Book of the Abacus”, the first European work on Indian and Arabian mathematics. Liber abaci book was based on the arithmetic and algebra and introduced the Indian-Arabic place-value decimal system and the use of Indian-Arabic numerals into Europe. It also introduced simultaneous linear equations.