How did the concept of deduction set ancient Greek mathematics apart from ancient Egyptian mathematics? Discuss specific mathematical principles known to each civilization.

For this assignment, you will write a “guided” essay on one of the following topics. Use the McClellan and Dorn text as your starting point and effectively use at least one other scholarly source. Need help identifying appropriate resources? Use this APUS Library Online Research page to help.

Topic Choices:

A) How did the concept of deduction set ancient Greek mathematics apart from ancient Egyptian mathematics? Discuss specific mathematical principles known to each civilization.

Guided Essay:

1. Start with an introduction: this should be at least 3-5 sentences that summarize the main idea behind your essay. You will identify which topic you selected and make your main point.

2. Next you move into the body of your essay. Here you will write at least 3 paragraphs that outline specific evidence supporting your main point.

3. Finally, wrap it all up in a nice conclusion. This will be at least 3-5 sentences that summarizes your main point and evidence. Do not just repeat your introduction or use exact sentences from your body paragraphs.

4. Finish with references! Ideally, we want to practice APA formatting, so try to provide your references in that format. This APA Style Guide webpage is a great primer on APA formatting.

Resources to use:

https://ebookcentral.proquest.com/lib/apus/reader.action?docID=3318261

https://ebookcentral.proquest.com/lib/apus/reader.action?docID=4385979

Ancient Greek Mathematics
When we think about ancient mathematics, the Ancient Greeks spring to mind as the founders of the calculations we use everyday. The work of the great Ancient Greek mathematicians pervades every part of life, from sending rockets into space to accounting, and from architecture to DIY. The Greek deductive approach to mathematics is probably the greatest legacy that they passed onto the world, and is one of the foundations of modern society.

### The Origins of Ancient Greek Mathematics

#### Thales (C467 BCE – 497 BCE)

Even the great theoretical physicists such as Stephen Hawking are steeped in the work of the Greeks, as the foundation of their elegant theories about how the universe works. Mathematicians such as Pythagoras, Euclid, and Archimedes are still familiar to us, over two millennia later, and their work is still taught in schools and colleges around the world.

The Greeks took a lot of their methodology and techniques from the Babylonians and Egyptians, as even Plato was happy to admit, but the Greeks were the first to move math into the realm of theory, reasoning and deduction rather than measurement. The Egyptians tended to use mathematics for practical purposes and used brute force to solve problems; for example, they were not bothered about finding an exact number for Pi and, as long as it served their purposes, an approximate value sufficed.

The Babylonians looked at the relationships behind numbers a little more than the Egyptians, but even their slightly more abstract work was largely empirical in nature.

The Greeks changed this by looking for underlying rules and relationships governing numbers and functions. They believed that, because the universe was perfect, they could use deductive reasoning to establish mathematical facts, without the impurity of inaccurate empirical measurements. This shift in focus fueled the great advances they made in geometry, algebra and calculus, and mathematical reasoning even became the basis of logical arguments.

Thales of Miletus earned his place in history as the first of the Greek mathematicians, although he is often unfairly overlooked in favor of Pythagoras, Archimedes and Euclid. Because we have no primary sources describing his contributions, we have to rely upon later mathematicians to fill in the details. Although his contribution was undoubtedly immense, this lack of information prevented him from becoming as influential as Euclid or Pythagoras, whose texts were studied by the great Islamic and Renaissance scholars.

Thales Theorem – the base angles of an isosceles triangle are equal (Creative Commons) |

As a student, Thales traveled to Egypt and learned all that he could from the scholars there about trial and error methods for solving mathematical problems and astronomy.

He soon began to surpass his teachers and began to question how the numbers fitted together, believing that these trial and error methods lacked elegance and verification. It is rumored, although not substantiated, that he also traveled to Babylon: Even if not, it is likely that the work of the Babylonian mathematicians was available to him.

Upon returning to Greece, Thales set up a school to teach others what he knew and tried to establish axioms (mathematical proofs). Once these first principles were in place, he reasoned that all other mathematical laws could be deduced. His four main mathematical proofs were:

- The diameter of a circle exactly bisects the circle
- The base angles of an isosceles triangle are equal
- The two pairs of angles formed by two intersecting lines are identical
- If one side and the two adjacent angles of a triangle are shared by another triangle, the triangles are identical.