Mathematics and Historical Foundation of Mathematics

A Discussion of a Couple Ancient Numeration Systems

If you were to chose between the Babylonian Number and the Egyptian Number Systems, which would you chose? 

Egyptian:ancientegyptianfacts.com

Babylonian:kreannasandoval.wordpress.com

After some reading, and contemplation I decided that I would favor the Babylonian over Egyptian for the main reason that Babylonian has much less symbols to memorize.  The Egyptian numbers require many symbols for even simple and smaller numbers. The Babylonian system is a more simple way to represent numbers because there aren’t as many symbols, they’re just repeated to represent the bigger numbers.  There’s also a simpler way to represent numbers involving a way to represent a number minus one.  It involves simply placing a certain symbol before the other symbols rather than after.  That is another advantage of the Babylonian system, is that it is read left to right, and if we were required to switch number systems at this time, that would be an easier transition. The Egyptian is read right to left.  The Babylonian system uses a base 60 rather than base 10 like we do in our current system. The Egyptians do not have a base system, so that is part of why they have to create so many more symbols and hieroglyphs.  So although the transition to a base of 60 would be difficult and confusing, I think it’d be better than a transition to a number system with no base system at all.

What is The Rhind Papyrus?

                                                   https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

The Rhind Papyrus is a long scroll discovered in Thebes, Egypt that gives us insight to what mathematics the ancient Egyptians performed.  From what we can tell, the most mathematics that the Egyptians did was practical problems involving money managing, creating the calendar, measuring and working with the Nile River, and proportioning food.  It is what we now call applied arithmetic. The Egyptian number system is an additive number system. Rather than creating symbols and functions for multiplication, they added the numbers repeated times. Then to divide, they would do multiplication in reverse.  When dealing with fractional numbers, the Egyptians would only use 1 as a numerator, making representations of a fraction much longer.  We think that the Egyptians didn’t ever get around to proving anything, or creating theorems to be proved because of the amount of time and work it would take to complete practical problems. That was the Rhind Papyrus is mostly composed of, practical problems. The Egyptians dipped into algebra by solving some problems dealing with only one variable that were fairly simple.  Their methods of solving these algebraic problems are longer and more complicated than what we do now with everyday algebra, but they are very interesting and I think it’s quite incredible that they were able to come up with this and make it work. For example, one of their methods is the method of double false position. Ultimately, you guess two solutions to the problem, plug them back into the equation and use the guesses and the solutions when the guesses were plugged into the problem to compute the correct solution.   I think it’s really exciting and interesting to learn about the way that these people came up with solutions to their problems. Their methods are different, but ultimately they mean the same things as what we do now to solve problems, and I think that’s pretty darn cool. 

My Favorite Mathematician

Descartes marked the beginning of pulling mathematics back out into the picture after the centuries of dark ages when mathematics were deemed unimportant. Rather than only utilizing mathematics for application such as basic finances and arithmetic, he pursued mathematics in a more pure form. He wanted to be able to logically and mathematically deduce all types of propositions from the most basic principles such as axioms or self-evident truths.  In accordance with that, he wanted to be able to define absolute truths that could not be countered. His ideas greatly impacted and influenced the start of the debate between faith and reason. 

www.edublox.com

He also contributed to the new and coming ideas and theories involving the nature of the universe. He argued against the Aristotelian and Ptolemaic view about the universe. He believed that mathematics and mechanics were the backbone to true and certain laws of nature. His theory about the universe was that the sun is at the center of a vortex and that is how the planets revolve about the sun. Although this theory had major holes and could not be proven, it was influential in increasing the study and discovery of the universe beside theologian beliefs and the theories of the Christian Church.

One of Descartes’ most well-known contributions to modern mathematics is his discovery of the coordinate plane.  This is why the coordinate plane that is most commonly used is called “Cartesian coordinates.”  Descartes certainly wasn’t the only mathematician to really officially formalize Cartesian coordinate geometry, in fact, he only really worked with the first quadrant of the plane (only positive x and y values.) But he was able to begin to piece together the notations and concepts of both algebra and geometry.  This means that he could represent geometrical figures on a Cartesian graph. This way, instead of writing a segment from point A to point B, he could represent this as an algebraic line.  Then with the segment graphed as an algebraic line, he was able to prove theorems easier and be able to measure lengths, distances, areas, etc., of all sorts of shapes in a more algorithmic way that was more accessible to people including those who were not skilled mathematicians.