Seminar Writing Questions
Mathematical Systems, Fall 2005
- What did you find interesting of Descartes's work?
- How has the motivation for mathematical discovery changed
from the beginning of the book through Chapter 10? (Consider
Roberval's obsession with getting credit.)
- In reading this book, have you noticed any biases?
- What do you like about the book; what don't you?
- What is Mathematics?
- What led to the mathematical and scientific eruption of the 17th
- To what extent did the invention of the telescope change the
development of astronomy in the 17th century?
- Explain figure 80 on page 331.
- What were Galileo's discoveries that proved Aristotle's theory
- How did Western Europe reacquire knowledge of Greek mathematics?
- How did the printing press "popularize" mathematics?
- What do you think the most important factor in the growth of
mathematics between 500-1500 was?
- How does the development of smilar mathematical relations/properties
by cultures seemingly independent of one another influence your
opinion of whether math was "invented" or "discovered"?
- Explain why the diagram on the bottom of page 224 works.
- What are some differences between Greek and Hindu maths?
- How have mysticism/religion affected (detrimentally/beneficially)
the progress of mathematics?
- If you could meet any of the mathematicians from this chapter,
which would you meet and why?
- Who determined the length of the man lunar month to within 1"
of the present accepted value?
- What is the difference between postulates and axioms?
- If you had to read one of Euclid's books, which one would it
be and why?
- Why spend 10 years making a 65,537-gon instead of a 65,538-gon?
- Why is Euclid important? What did he do for mathematics?
- What advances made it easier for mathematicians to calculate the
digits of pi? Why do people still look for the digits even though
it has been proven to be irrational and transcendental?
- In 1767, Lambert showed that pi is irrational. But in 1892, a writer
proclaimed pi = 3.2. Many others have tried to give absolute figures
for pi. What compels these so-called "circle-squarers"?
- Do you agree with Plato's philosophy on mathematics? How does the
fact that Plato himself was not a mathematician influence your
- What discovery rocked the Pythagorean world? Relate this to
what we've been studying in class lately.
- How many even perfect numbers have been discovered when n is less
than 5000? List the first 3 and last 2 discovered.
- What are some possible applications of the various Pythagorean
number classifications? (perfect, amicable, etc.)
- Are algebraic solutions better than geometric ones? Is the algebraic
approach better? Why or why not?
- What reasons did the book give for more advanced mathematics
in ancient Babylon?
- On p. 55 two symbols are identified for addition and subtraction.
- Identify these.
- Why do these make sense (or not)?
- How could they relate to mensuration?
- Propose symbols in the same style for: equals, zero, unknown,
- What would the advantages and disadvantages of using base 2 instead
of base 10 be?
- Is positional notation actually better than other number systems?
Why or why not?
- Invent a discussion question and answer it.
Brian L. Walter