By know if you are reading this you know that this web project consists of three sections. The three sections are divided by an era in which each scientist worked in. The ancient episode was devoted to the Sand-Reckoner a work by Archimedes, the medieval section was devoted to the Fibonacci Sequence which was made famous by Leonardo of Pisa, also known as Fibonacci, and the early intermediate episode was devoted to a modern interpretation of Kepler’s three laws of planetary motion. Each scientist that is motioned in each episode was some sort of mathematician. Each scientist was a mathematician, but the works from each scientist was quite different from the next. The one area of interest that each scientist has in common with the next is a subfield of mathematics called geometry. The following paragraphs are brief overviews of each episode.

The first episode is devoted to Archimedes and his work the Sand-Reckoner. Archimedes was a scientist that was not only a mathematician, but a physicist as well. He studied most areas of mathematics that had been known in his time, and he also used mathematics to explain mechanics, which was very similar to the mathematical approach in introductory physics courses today, and optics which are fields in physics. In the Sand-Reckoner, Archimedes used logic to show that the grains of sand contained in the universe are indeed finite, while developing a notation that was capable of representing very large numbers past the limit of the number myriad. Archimedes used a series of geometric arguments as well as distances and quantities that gave the quantity of sand in a given volume. Archimedes then calculated the volume of the universe and determined a finite number for the grains of sand contained in the universe using his new numerical notation.

The second episode is devoted to the Fibonacci Sequence, which was the solution to a problem which was presented by Leonardo of Pisa, also known as Fibonacci, presented in his book the Liber Abaci. The Fibonacci sequence is directly related to a number called the golden ratio. It just so happens that the Fibonacci Sequence defines the golden ratio. The golden ratio is found in seemingly endless cases in nature. I have shown some relations with geometric objects which are defined by the golden ratio, mainly the squaring of rectangles. The special case of the squaring of rectangles in which the ratio of the sides of the rectangles is the golden ratio, then you can obtain the logarithmic spiral from the golden rectangle. I posted several pictures that presented a logarithmic spiral in nature.

The third episode is devoted to the mathematician and astronomer Johannes Kepler. Kepler’s three laws of planetary motion are explained from a modern perspective. I was unable to interpret his original works and find the now three laws of planetary motion. I first described Kepler’s laws and then explained gravity according Newton’s laws of universal gravitation, because Kepler’s three laws of planetary motion is mainly a mathematical argument. I then appliedNewton’s laws of gravity to Kepler’s laws to yield the accepted three laws of planetary motion.

Thank you for reading my web project. I hope you have understood a little bit more about mathematics and along the way I hope that you enjoyed at least some areas within my project.