Archimedes was a great mathematician of ancient times. His greatest contributions were in geometry. He also spent some time in Egypt, where he invented the machine now called Archimedes' screw, which was a mechanical water pump. Among his most famous works is Measurement of the Circle, where he determined the exact value of pi between the two fractions, 3 10/71 and 3 1/7. He got this information by inscribing and circumscribing a circle with a 96-sided regular polygon. Archimedes made many contributions to geometry in his work on the areas of plane figures and on the areas of area and volumes of curved surfaces. His methods started the idea for calculus which was "invented" 2,000 years later by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. Archimedes proved that the volume of an inscribed sphere is two-thirds the volume of a circumscribed cylinder. He requested that this formula/diagram be inscribed on his tomb. His works (that survived) include:

Measurement of a Circle

On the Sphere and Cylinder

On Spirals

The Sand Reckoner

The Roman’s highest numeral was a myriad (10,000). Archimedes was not content to use that as the biggest number, so he decided to conduct an experiment using large numbers. The question: How many grains of sand there are in the universe? He made up a system to measure the sand. While solving this problem, Archimedes discovered something called powers. The answer to Archimedes' question was one with 62 zeros after it (1 x 1062).. When numbers are multiplied by themselves, they are called powers. Some powers of two are:

1 = 0 power=20

2 = 1st power=21

2 x 2 = 2nd power (squared)=22

2 x 2 x 2= 3rd power (cubed)=23

2 x 2 x 2 x 2= 4th power=24

There are short ways to write exponents. For example, a short way to write 81 is 34.This is read as three to the fourth power. On Plane Equilibriums

On Floating Bodies This problem was after Archimedes had solved the problem of King Hiero’s gold crown. He experimented with liquids. He discovered density and specific gravity.

Copernicus

Copernicus, Nicolaus (1473-1543), Polish astronomer, best known for his astronomical theory that the sun is at rest near the center of the universe, and that the earth, spinning on its axis once daily, revolves annually around the sun. This is called the heliocentric, or sun-centered, system. See Astronomy; Solar System. Early Life and Education

Copernicus was born on February 19, 1473, in Thorn (now Torun), Poland, to a family of merchants and municipal officials. Copernicus's maternal uncle, Bishop Lukasz Watzenrode, saw to it that his nephew obtained a solid education at the best universities. Copernicus entered Jagiellonian University in 1491, studied the liberal arts for four years without receiving a degree, and then, like many Poles of his social class, went to Italy to study medicine and law. Before he left, his uncle had him appointed a church administrator in Frauenberg (now Frombork); this was a post with financial responsibilities but no priestly duties. In January 1497 Copernicus began to study canon law at the University of Bologna while living in the home of a mathematics professor, Domenico Maria de Novara. Copernicus's geographical and astronomical interests were greatly stimulated by Domenico Maria, an early critic of the accuracy of the Geography of the 2nd-century astronomer Ptolemy. Together, the two men observed the occultation (the eclipse by the moon) of the star Aldebaran on March 9, 1497. In 1500 Copernicus lectured on astronomy in Rome. The following year he gained permission to study medicine at Padua, the university where Galileo taught nearly a century later. It was not unusual at the time to study a subject at one university and then to receive a degree from another—often less expensive—institution. And so Copernicus, without completing his medical studies, received a doctorate in canon law from Ferrara in 1503 and then returned to Poland to take up...