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Weekly QuizDemonstrate a fearless pursuit of *auk*ademic*auk*cellence by plunging, head-first of course, into these questions. Return every week for another quiz on one of the 14,000 topics in the Knowledge Master Library.

**History of Mathematics**(Click on the question number for the answer.) 1. B **Numerals**

The numerals used by today's mathematicians were developed in ...

A. Rome

B. Arabia

C. France

D. Greece

E. England

2. binary system **Letters from Leibnitz**

To what system was Leibnitz referring when he wrote this?- I enclose an attempt to devise a new numerical

system. By basing it on the number 2 instead

of the number 10, I am able to write all

numbers in terms of 0 and 1.

3. C **Integer Sets**

What set of positive integers satisfies the equation, a squared + b squared = c squared?

A. trigonometric identities

B. Cartesian coordinates

C. Pythagorean triples

D. Fibonacci sequences

E. ordered pairs

4. pi **Archimedes**

Archimedes described it as greater than 3 10/71 and less than 3 10/70. Today that number is called ...

5. A **Ancient Units**

Which ancient Egyptian unit of measurement was set as the distance between the elbow and the tip of the middle finger?

A. cubit

B. stone

C. karat

D. quire

E. parsec

6. 60 **Number Systems**

Computers use the binary system. We ordinarily use the decimal system. But the Babylonians used the sexagesimal system that had what number as its base?

7. C **Fancy Figurin'**

Who deduced the heights of the pyramids from the lengths of their shadows and measured the distance to a ship from shore by the method of similar triangles?

A. Plato

B. Galen

C. Thales

D. Pericles

E. Euripides

8. abacus **Calculators**

This ancient device was a predecessor of the modern calculating machine and is still widely used in Japan and China. It consists of a set of beads on rods with each rod denoting place value. Name this instrument.

9. E **Polymaths**

Who collaborated with Alfred North Whitehead in writing "Principia Mathematica" and later won the 1950 Nobel prize for literature?

A. M.C. Escher

B. Jean Wourier

C. Norbert Weiner

D. Leonhard Euler

E. Bertrand Russell

10. Euclid **Ancient Axioms**

Name the Greek who said these things.- All right angles are equal to one another.

A finite line segment can be extended

to a line of any length.

11. B **Literary Logicians**

Who was a mathematician and writer?

A. Pat Carroll

B. Lewis Carroll

C. Leo G. Carroll

D. Diahann Carroll

E. Madeline Carroll

12. meter **History of Measurement**

The distance from the North Pole to the equator was measured along an arc of a great circle, and this unit was repeatedly divided by ten until what convenient unit was determined?

13. A **Math Fundamentals**

What concept was developed by ancient Hindu mathematicians?

A. zero

B. conic section

C. decimal point

D. 360-degree circle

E. Pythagorean theorem

14. E **Special Numbers**

Ancient Greeks said a natural number is perfect if the sum of all its divisors except itself equals the number. Which number is perfect?

A. 4

B. 9

C. 16

D. 20

E. 28

15. logarithms **Math Tools**

John Napier introduced what system of notation as a computational tool in 1614?

16. B **Syllogisms**

Who invented the syllogism as the keystone of his system of deductive logic?

A. Ptolemy

B. Aristotle

C. George Boole

D. Sir Francis Bacon

E. Nikolai Lobachevski

17. E **Round and Round**

The 360-degree circle and the 60-minute hour were developed by the ...

A. Greeks

B. Mayans

C. Romans

D. Egyptians

E. Babylonians

18. circumference of the Earth **Simple Solutions**

In 200 B.C., Eratosthenes found the Sun's rays were vertical at Syene and 7 1/2 degrees from vertical at Alexandria. He knew the distance between the two cities. What was he able to calculate using these data?

19. B **Founders**

August F. Mobius was a founder of what branch of mathematics?

A. calculus

B. topology

C. probability

D. game theory

E. symbolic logic

20. ten **The Abacus**

Each row of beads on an abacus stands for a different power of ...

21. C **Chronology of Math**

Which field of mathematics was developed first?

A. algebra

B. trigonometry

C. deductive logic

D. analytic geometry

E. probability theory

22. D **Calculus**

The development of differential and integral calculus is attributed to ...

A. Kepler and Fermi

B. Maxwell and Gauss

C. Russell and Wiener

D. Newton and Leibnitz

E. Oughtred and Mosely

23. George Boole **Computer History**

Name the contemporary of Charles Babbage who developed a symbolic logic that reduced all logical relationships to these three expressions.- and or not

24 B **Graphing**

The means of graphically representing functions of variables occurred with the introduction of coordinates by what mathematician?

A. Isaac Newton

B. Rene Descartes

C. Norbert Wiener

D. Leonhard Euler

E. Leonardo Fibonacci

25. Zeno **Paradox Posers**

What Greek philosopher born in Elea in the fifth century B.C. is known by mathematicians for his paradoxes that appear to demonstrate the impossibility of movement?

26. C **Machines**

A device, ENIAC, was the first ...

A. abacus

B. compass

C. electronic computer

D. mechanical slide rule

E. gear-driven calculator

27. C **Math Techniques**

The Sieve of Eratosthenes is used to find ...

A. vectors

B. cube roots

C. prime numbers

D. irrational numbers

E. an approximation of pi

28. Kurt Godel **Limits to Logic**

What Austrian-born mathematician demonstrated that there can be no proof of the consistency of a formal mathematical system from within that system?

29. D **Math Centuries**

During what century did Newton and Leibnitz develop calculus and Descartes invent analytic geometry?

A. 16th

B. 12th

C. 19th

D. 17th

E. 14th

30. D **Solids**

Which is not one of the five Platonic solids?

A. hexahedron

B. octahedron

C. tetrahedron

D. pentahedron

E. dodecahedron

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**Answers to Math History**- 1. B
- 2. binary system
- 3. C
- 4. pi
- 5. A
- 6. 60
- 7. C
- 8. abacus
- 9. E
- 10. Euclid
- 11. B
- 12. meter
- 13. A
- 14. E
- 15. logarithms
- 16. B
- 17. E
- 18. circumference of the Earth
- 19. B
- 20. ten
- 21. C
- 22. D
- 23. George Boole
- 24. B
- 25. Zeno
- 26. C
- 27. C
- 28. Kurt Godel
- 29. D
- 30. D
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