Math 311. Final Exam. Name:____________________________
4 May 1989. Prof. Rickey
N.B. If you feel a question is ambiguous or you want to justify the answer you
give, feel free to include a note of explanation.
I. Since everyone thinks true-false questions are too tricky, let's try a
Newton-Leibniz question. (10 pts)
N L 1. Did his work on the calculus first.
N L 2. Published his work on the calculus first.
N L 3. Worked with the harmonic triangle.
N L 4. Built a calculating machine.
N L 5. Worked at the mint.
N L 6. Had the better notation for the calculus.
N L 7. Halley encouraged him to publish.
N L 8. His followers did the better work.
N L 9. Discovered the general binomial theorem.
N L 10. Built a telescope.
II. Arrange the following names in chronological order according to when their
most significant work was done, using 1 for the earliest and 10 for the most
recent (If in doubt, draw a graph): (10 pts)
___ Fermat
___ Galileo
___ Khayyam
___ Recorde
___ Euler
___ Tartaglia
___ The Bernoulli Brothers
___ Al-Khwarizmi
III. Match each item in the second column with the one in the first column that
corresponds most closely. (35 pts)
A.
___ Gregorius
1. Analysin des Infiniment Petits.
___ Fibonacci
2. Opus geometricum
___ Cardano
3. Liber abaci
___ Descartes
4. The Whetstone of Witte
___ L'Hospital
5. Philosophiae naturalis principia mathematica
___ Newton
6. La Geometrie
___ Record
7. Ars magna
B.
___ Khayyam
1. Inventor of logarithms.
___ Gauss
2. Solved cubic equations geometrically.
___ Lindemann 3. The
stammerer.
___ Stevin
4. Showed π transcendental.
___ Napier
5. Constructibility of regular polygons.
___ Tartaglia
6. Decimals
___ von Schooten 7. Translator and expositor
of Descartes' work.
C.
___ Euler
1. Solved the cubic equation.
___ Bernoulli
2. Solved the quartic equation.
___ Cardano
3. Found the volume of an infinite solid.
___ Ferarri
4. Suggested the name calculus integralis.
___ Newton
5. An algebraist killed by the use of snuff
___ Harriot
6. The binomial theorem.
___ Torricell
7. The most prolific mathematician
D.
___ Bernoulli
1. Published the first calculus book.
___ Cardano
2. Hub of a correspondence network.
___ Fermat
3. First to recognize complex numbers.
___ Rolle
4. Discovered L'Hospital's rule.
___ L'Hospital
5. Introduced the equality sign.
___ Mersenne
6. An early critic of the calculus.
___ Recorde
7. Had a method of tangents.
E.
___ Aristarchus 1. De
revolutionibus orbium coelestium
___ Apollonius 2. The
almagest
___ Bombelli
3. Solved equations in integers
___ Copernicus 4. The
conics
___ Diophantus 5. On the
Size and Distance of the Sun and Moon
___ Eratosthenes 6. On the Measurement
of the Earth
___ Ptolemy
7. The irreducible case of the cubic
IV. Short answer questions. (45 pts)
1. Why are the Arabs important to the history of mathematics?
2. What does the word "quadrature" mean? Doesn't "quad-" mean 4?
3. Name several curves introduced in the seventeenth-century and explain why
they are important in the history of Mathematics?
4. State two of Kepler's laws.
5. What is a subtangent?
6. State Cavalieri's Principle.
7. Distinguish between Johann and Jakob Bernoulli by mentioning some things
about them and what they did.
8. What is a fluxion?
9. If you were introducing analytic geometry in a class, what would you say
about who, when, and why it was invented?
V. Answer both of the following Essay Questions. (50 pts)
1. What benefits, if any, are derived from knowing the history of mathematics?
You may answer both from an individual point of view and from the point of view
of future teacher. (Continue on back.)
2. If you were teaching high school algebra what points about the history of the
subject do you think it is important to tell the students about?
VI. (Optional; answer on back) If you studied "all the wrong stuff" for this
exam, tell me what questions you were prepared to answer and how you would have
answered them.