1. What London shopkeeper published a pamphlet called the Natural and - - PDF document

• 1. What London shopkeeper published a pamphlet called the Natural and Political Observations

Made Upon the Bills of Mortality?

• 2. Of the observations listed below, which one was not made from the 17th century study of the

Bills of Mortality?

• a. More males than females are born.
• b. Women live longer than men.
• c. More children are born in odd years than in even ones.
• d. The annual death rate is fairly constant (except for epidemic years).
• 3. The mathematical study of life expectancies and other demographic trends is called:
• a. Political arithmetic
• b. Actuarial science
• c. The Law of Large Numbers
• d. Theory of Probabilities
• 4. The first comprehensive book on statistics and probability was published in 1713 and written by

whom?

• a. Jakob Bernoulli
• b. Johann Bernoulli
• c. John Graunt
• d. William Petty
• 5. Statistics is still considered to be a branch of mathematics.
• 6. Which group of polyhedrons contains regular triangles for faces?
• a. hexahedron, dodecahedron, icosahedron
• b. tetrahedron, octahedron, icosahedron
• c. tetrahedron, hexahedron, dodecahedron
• d. icosahedrons, octahedron, dodecahedron
• 7. Which mathematician came up with the relationship of Platonic solids to elements of the

physical world?

• a. Kepler
• b. Archimedes
• c. Pythagoras
• d. Plato
• 8. Match the physical elements with the polyhedron they were thought to represent

___ Fire a) dodecahedron ___ Water b) hexahedron ___ Earth c) octahedron ___ Air d) tetrahedron ___ Universe e) icosahedron

• 9. Which Archimedean Solid is most common in everyday use? State the formal name and the

common name.

• 10. True/False: In the Platonic solids, a.k.a. regular polyhedron…

____ At least 5 polygonal faces must meet to form a vertex ____ The situation at each vertex is the same. ____ Sum of face angles at each vertex must be = 360° ____ Angle sum at each vertex divides evenly into the number of faces meeting at it

• 11. Which ancient civilization is credited with initially implementing a rectangular grid system and

how did they use it?

• 12. Which ancient Greek related some kinds of curves to the solution of numerical proportions?
• 13. Which late 16th century mathematician took a giant step towards focusing the power of algebra
• n the problems of geometry by representing quantities with letters and relationships with

equations?

• 14. Who published an expanded version of la geometrie?
• 15. Who was the French mathematician who developed many of the key concepts of analytic

geometry by 1630?

• 16. Who was the Greek astronomer who began working with chords?
• 17. Ptolemy’s book ______________ proved basic theories of chords.
• 18. Ptolemy provided a theorem that gives the sum and difference formulas of chords. Write the

mathematical statement of the theorem.

• 19. How was the Arabic’s trigonometry sophisticated?
• 20. How did Leonhard Euler effect how people thought of sine?
• 21. True or False Leibniz’s calculating machine the Stepped Reckoner used binary numeration in its

calculations.

• 22. When P is false and Q is true, which statement is true:
• a. P and Q
• b. P or Q
• c. P implies Q
• 23. Write out the following statement using symbolic logic. Don’t forget to assign a P and Q.

I stepped on a crack, but did not break my mother’s back

• 24. Write down both forms of De Morgan’s Law.
• 25. Explain what C. S. Pierce described as the difference between Mathematicians and Logicians.
• 26. The sum of the measures of the angles of a triangle varies based upon which type of geometry

you are. List the sum of the measures of the angles of a triangle for each of the following types

• f geometry.
• a. Euclidean geometry: ____
• b. Lobachevskian geometry: ____
• c. Riemannian geometry: ____
• 27. Which of the following is the parallel postulate?
• a. Through a point not on a line, there is exactly one line parallel to the given line.
• b. If a straight line falling on two straight lines makes the sum of the interior angles on the

same side less than two right angles, then the two straight lines if extended indefinitely meet on that side on which the angle sum is less than two right angles.

• c. If a straight line falling on two straight lines makes the sum of the interior angles on the

same side equal to two right angles then the two straight lines extend indefinitely and will never meet on either side.

• d. If two straight lines are cut by a transversal and the sum of the measure of the interior

angles equals 180, then the two lines will never intersect, thus making them parallel.

• 28. True or False: Saccheri was able to create a very convincing proof that showed if the negation of

the parallel postulate was an axiom, there was a contradiction in the system; thus, everyone believed the parallel postulate was able to be proven from the other postulates and this was taught for almost 100 years until Gauss came along.

• 29. Match the following mathematicians to their contributions to the Non-Euclidean geometry.
• a. Euclid
• 1. Concluded that the parallel postulate cannot be

proven from the other four postulates of Euclid

• b. Proculus
• 2. Wrote a logically equivalent statement to the parallel

postulate that would be easier to work with

• c. Playfair
• 3. Pointed out flaws in Ptolemy’s proof of the parallel

postulate and then tried to prove it himself

• d. Saccheri
• 4. Observed that extended continuously did not

necessarily imply infinitely long and used this fact to create a new system of geometry

• e. Lobachevsky
• 5. Wrote axioms of geometry which included the

parallel postulate

• f. Riemann
• 6. Tried to prove the parallel postulate could be proven

from the other four axioms by using its negation as an axiom and arriving at a contradiction

• 30. For the following geometries, match the ratio of the circumference, C to the diameter.
• a. Euclidean geometry
• 1. Greater than π
• b. Lobachevskian geometry
• 2. Exactly π
• c. Riemannian geometry
• 3. Less than π
• 31. If a fair six sided die is tossed one time what is the probability that it will not be 6?
• 32. Offered 1 chance to throw die, if 6 get $10, if 3 get $5, if anything else nothing. How much do

you pay to play?

• 33. Who was the first mathematician to look into probability?
• 34. put the following mathematicians in order by discoveries in probability.

Girolamo Cardano, Christiaan Huygens, Jakob Bernoulli, Chevalier de Mere, Blaise Pascal, Pierre de Fermat, Pierre-Simon Laplace

• 35. Who wrote Ars Conjectandi (“The art of Conjecture")?
• 36. Match the inventor with their calculating device
• a. John Napier
• 1. Arithmometer
• b. Blaise Pascal
• 2. Stepped Reckoner
• c. Gottfried Leibniz

3.Difference Engine

• d. Charles de Colmar
• 4. Pascaline
• e. Charles Babbage
• 5. Napier’s Bones

• 37. What is the binary number for the decimal number 3?
• a. 101
• b. 010
• c. 01
• d. 11
• 38. What was the first American computer called?
• 39. What is the name of the calculating device that is made up of beads and rods and is also

referred to as the counting tray?

• 40. Who founded the Tabulating Machine Company, which later became known as IBM?