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The 14 questions are short, but substantive answer questions and have a source f

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The 14 questions are short, but substantive answer questions and have a source for each one.
Does the development of personal knowledge of mathematics mirror the historical development of the subject? That is, do we learn mathematical concepts as individuals in the same order in which these concepts appeared historically?
What are the differences in the counting systems used in ancient China, Egypt and Mesopotamia? How did counting systems evolve throughout time?
Both the Egyptians and Greeks used a sexagesimal system even though the Mesopotamians had found and used the place-value system. Why do you think they used this more complex system? Along the same lines in modern society we have the metric system which uses base 10 and would be simplest, so why do you think that the United states has not adopted this system. Is there a benefit to the sexagesimal system and the one we currently use for measurement?
In what way does ancient Greek mathematics differ from the mathematics of Mesopotamia and Egypt?
Archimedes has a reputation as the greatest mathematician of antiquity and one of the three greatest of all time. What criteria can you imagine being applied to justify this judgement? Who else would you think would make the top three mathematicians of all time? Please justify your answer.
Occasionally mathematicians/scientists will manipulate their data to fit their theory. Give an example of such a situation when the manipulation was inaccurate and one where the result was accurate. Discuss the results of these situations. What is the benefit of such behaviors?
What differences do you notice in the “style” of mathematics in Greece and India? Consider in particular the importance of logic, the metaphysical views of the nature of such things as lines, circles, and the like, and the interpretation of the infinite. What are the benefits to each style?
Compare the trigonometry’s developed by Ptolemy and the Hindu mathematicians with each other and with trigonometry as we know it today. What significant differences are there between any two of them?
What kind of algebraic problems did the Chinese solve that were different from those discussed from other cultures?
Summarize the progress made on each of the three classical problems during the fourth century BCE. How were these problems approached in different cultures? Have the solutions changed?
How does projective geometry differ from Euclidean geometry?
Omar Khayyam criticized ibn al-Haytham for discussing a line that moves while remaining perpendicular to another line. Yet Newton used exactly the same language when discussing the center of curvature, and no one seems to have objected. What difference in mathematical culture does this contrast in points of view signify?
History is riddled with inaccuracies and misinterpretations, and mathematics history is no different. State one inaccuracy that you found in our studies. Tell what the inaccuracy was and why you think it occurred. Was there a benefit to altering the truth?
Describe an example of significant applications of mathematics to commerce, science, and general life. Pick an example from each commerce, science and general life but make sure that each example is from a different time period. Explain the example, how mathematics contributed to its discovery and the value it played in the lives of the people of that time period.

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