Cultural Essay 6
Ancient and Medieval China made many mathematical advancements but in different ways that other such as the Greeks did by focusing more on colors, symbols and really shapes of the problems. In order to be able to use such general ideas, many trials, errors and corrections had to be made. For example, when solving calculations with numbers, horizontal and vertical lines were used to combine numbers together but alternated directions to keep their place holders. Then the color of the result represented whether or not the final integer was positive or negative.
Example
=”llll ≡ l → 2431″
To solve square roots, gnomes were used by first getting to the nearest squared value and then taking the remainder and creating another gnome to get an even smaller value. At this step, different values are guess for the variable and tried until the right number is picked to equal the remainder value. As one could see, this takes many attempts to get the right value however with practice and educated guesses, this method became less tedious to solve for. Although the credit will later go to a man by the name of Hornon, in about 1050 C.E., Jia Xian formulated a process to use when dividing two polynomials with variables and exponents. This is today known as long division with is still taught in secondary schools. As we know with long division, it takes multiple steps to get the correct and final answer, even then with a remainder value. The same is true of Modular Arithmetic which tries to find the smallest integer when dividing a number and getting a certain remainder value. One starts by putting equations in the correct form, solving for a variable, substituting for that variable and solving for a second variable and so on until the number value is found.

Reflective Tag
I found Modular Arithmetic to be very intriguing. Although I’m not sure why it was used in this day and time or what it may physically be applied to in the real world, it is like a puzzle to be solved or a game to me and is very addicting to want to solve a problem. The comparison of arithmetic and mathematics between the Greeks and Egyptians is very thought provoking to me. Clearly the cultures were different and the two areas were separated by vast amounts of varying territories, but I cannot help but marvel at the level of human intelligence that is alive for these two cultures to find two different methods to solve the same problems and for both of them to work. It truly is miraculous and worth noting and learning about.