Math 2008/7008 Test 2

Reasoning tables had horizontal lines and a vertical line, the thousands place was marked by a cross

How did our comma use in 1,000 come about?

Self-educated by reading parent's library

How was Sophie Germain educated?

Pyramid of Kukulkan which has 4 stairways of 91 steps each, with platform at top (365)

Where else can the Mayan number system be seen?

India because resemblance of Brahmi numerals with our 6,7,8,9

Where is it thought our digits originated? Why?

Egypt in Rhind Papyrus

Where was earliest use of multiplication seen?

John Napier for clerks

Who created an easy way to multiply large numbers? Why?

Thomas Harriot in An Analytical Praxis

Who created inequality sign? Where?

Blaise Pascal

Who designed adding machine?

Gauss, sent him her own mathematical findings after reading his work on number theory

Who did Sophie Germain start working with and how?

Pierre de Fermat

Who established the foundation of number theory?

Andrew J. Wiles of Princeton, twice because mistake in first

Who found the term-35 proof of number theorem? How many times?

Sophie Germain

Who was the founder of mathematical physics?

J.H. Rahn (up to 24,000) John Pell (up to 100,000) J.P Kulik (100,000,000)

Who were the three men responsible for coming up with lists of factors?

French use of 24 for 80

How can base 20 be seen in Celtics?

Successive doubling and then add the product for the doubles which add up to the factor you want (p 126 for example)

Describe Egyptian multiplication.

Created rods with multiplication facts for each digit, you line up the rods for the digits you need and add the diagonals

Describe the Egyptian multiplication method.

Brotherhood of mathematicians that thought numbers had special meanings

Describe the Pythagoreans.

Chart where you circle the prime numbers and then cross out all of its multiples, so only prime numbers are left circled

Describe the Sieve of Erstosthenes.

Dial a series of wheels with digits 0 to 9 and with number great than 9 and after 9 a ratchet moves to next wheel (each wheel is a place value in base-10)

Describe the adding machine.

Equal spacing between equal sign, but in greater than sign, there is greater distance between lines on greater than side

Describe theory behind design of the inequality sign.

Lincoln's Gettysburg address four score

How can base 20 be seen in American history?

Addition

Multiplication is just what other operation?

Babylonian number system

Name the number system in the image:

Egyptian number system

Name the number system in the image:

Mayan number system

Name the number system in the image:

Positive

The set of ______ fractions is closed for division.

True

True or False: Addition is Commutative

False

True or False: Subtraction of integers is commutative.

Maya, Aztecs, New Guinea, Celtics, Greenlanders

What cultures had based 20 (there are 6)?

Different color rays have different degrees of heat

What did Emile find out about color?

Her theory of numbers: impossible to solve for x, y, and z in last theorem if they are not divisible by odd numbers

What is Sophie Germain best known for?

No positive integer for n>2 such that xn + yn = zn but he didn't write proof

What is the number theorem? What was lacking?

1: reason 2: opinion 4: justice 5: marriage

What numbers had an aspect of life significance?

Top prize from French Academy of Science for best essay on mathematic laws of elastic surfaces

What prize did Sophie Germain win and how?

1+2+3+4 equals 10

What sum had significant meaning?

In Florence Hindu-Arabic banned so had to use Roman

What system did merchants use for digits and why?

Physics textbook which was originally on essay on physics for her son

What textbook did de Breteuil develop? How?

Study of fire proposing that light and heat have same cause and are modes of motion

What was Emile de Breteuil's first scientific work?

1, 2, 3, 4 are fire, water, air, and earth

What was linked to earth?

It established her competence among male colleagues

What was significance of de Breteuil's work?

Even were weak and earthly, odd were strong and heavenly

What was the difference between even and odd numbers?

Their knowledge of astronomy and 365-day calendar

What were Mayans known for?

Algorists (Hindu-Arabic and place value) vs abacist (Roman numerals, abacus)

What were the two opposing numeration systems in 15th and 16th century?

Spain in 976

When do you see our digits in Europe first?

The calendar which was 18 months of 20 days each (5 for holidays)

Where did the Mayan number system come from?