linda salgado troup middle school. mathematicians are people, too (volumes 1 and 2) reimer &...

Linda SalgadoTroup Middle School

Mathematicians Are People, Too (Volumes 1 and 2)

Reimer & Reimer, Dale Seymour Publications

Famous Problems and Their Mathematicians

Johnson, Teacher Ideas Press

A Peek Into Math of the Past

Voolich, Dale Seymour Publications

Hands-on Math for Middle Grades

Creative Teaching Press

Mr. Archimedes’ Bath, Pamela Allen

The Librarian Who Measured the Earth, Kathryn Lasky

What’s Your Angle, Pythagoras? Julie Ellis

The Fly on the Ceiling, Dr. Julie Glass

The History of Counting, Denise Schmandt-Besserat

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List of many websites

on mathematicians

Rene Descartes

France1596-1650Co-Founder of

Analytic Geometry

Combined algebra and geometry creating analytical geometry or coordinate geometry

First to use the last letters of the alphabet (x, y, z) for unknown quantities and the first letters of the alphabet (a, b, c) to designate known quantities.

X y z

Discovered how to calculate the volume of a sphere, and even wanted this diagram on his tombstone. He made so much progress in this area that nothing could be added for 18 centuries.

EUREKA (I have found it!) – Bouyancy

Developed Exponential system of writing large numbers

Discovered the Law of the Lever

x2

Italian postage stamp honoring Archimedes May 2, 1983

Scott Catalogue Number 1559

This statue in the National Museum in Naples, Italy, was widely claimed to

be Archimedes. It is actually a bust of Archidamos III,

a third century BC king of Sparta

Archimedes water screw

A 1740 engraving of Archimedes planning the

defenses of Syracuse. The Greek writing on his cap is

                     (Archimedes the geometer).

A detail of a wall painting in the Stanzino delle Matematiche in the Galleria degli Uffizi

in Florence, Italy.Painted by Giulio Parigi (1571-1635) in the

years 1599-1600.

Archimedes designed many

tools for defending Syracuse from

invasion. This is a model of how one

of Archimedeswar gadgets may

have worked.

Burning MirrorArchimedes used

mirrors to reflect and intensify the sun,

causing the ships to catch on fire.

Wall painting from the Stanzino delle Matematiche in the Galleria degli Uffizi (Florence, Italy). Painted by Giulio Parigi (1571-1635) in the years 1599-1600.

Engraving fromMechanics Magazine

London, 1824

Give me a place to stand and I will move the earth

The Law of the Lever

w2w1 d1 d2

fulcrum

w1 x d1 = w2 x d2

2 feet8 feet

?400 pounds

400 pounds

5 feet5 feet

?

w1 x d1 = w2 x d2 w1 x 8 = 400 x 2 w1 = 100

w1 x d1 = w2 x d2 w1 x 5 = 400 x 5 w1 = 400

Lever Problems• How long would the lever need to be so that you can lift

a 20 ton dinosaur? Place the dinosaur 10 feet from the fulcrum and pretend you weigh 100 pounds.

• How long would the lever need to be so that you can lift a team of 10 football players (weighing 200 pounds each)? Use the same set-up as above.

• How long would the lever need to be so that you can lift a lifetime supply of candy bars? Estimate that you can eat 2 pounds of candy each week for 70 years. Use the same set-up as above.

The death of Archimedes depicted on a Roman floor mosaic

Benjamin Franklin was a statesman and diplomat for the newly formed United

States, as well as a prolific author and inventor. Franklin helped draft, and then

signed, the Declaration of Independence in 1776, and he was a delegate to the

Constitutional Convention in 1787. As a civic leader, he initiated a number of new programs in Philadelphia, including a fire company, fire insurance, a library, and a

university.

Ben Franklin sitting on a bench. Artwork on the campus of the University of

Pennsylvania.

Ben Franklin discovered electricity, bifocal eye glasses, the odometer and a wood burning stove, among many

other things.

Arrange the numbers 1-9, using each number only once. All rows, columns and diagonals must

add to the same number

8 5 32 9 76 1 4

Arrange the numbers 1-9, using each number only once. All rows, columns and diagonals

must add to the same number

= 16

= 18

= 11

MEA

N =

15

8 1 6

3 5 7

4 9 2

15

= 15

= 15

= 15

15 15 15 15

Correct Answer

Multiply each

number by some integer…is it still a magic square?

Arrange the numbers 15-23, using each number only once. All rows, columns and diagonals must

add to the same number

15

16

17

18

19

20

21

22

23

171

171 ÷ 3 = 57each row, column, & diagonal

Benjamin Franklin’s Numbers

52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24

50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

1. Find the sum of any row: 2. Find the sum of any column: 3. Find the sum of the first four numbers of any row: 4. Find the sum of the last four numbers of any row: 5. Find the sum of the first four numbers of any column: 6. Find the sum of the last four numbers of any column: 7. Find the sum of the four corners: 8. Draw a box around a set of 16 numbers the make a 4x4

square. Find the sum of the corners of this square: 9. Draw a box around a set of 36 numbers the make a 6x6

square. Find the sum of the corners of this square: 10. Draw a box around any 4 numbers that make a 2x2 square.

Find the sum of the corners.

1 + 2 + 3 + … + 98 + 99 + 100 =

5050

Helped his father with payroll accounts at the age of 3

Remembers he could “reckon” before he could talk

Know seven languages by the age of 19

Proved construction of a 17 sided polygon with only a compass and straight edge, thought impossible

for 2000 years.

Gauss wanted a heptadecagon placed on his gravestone, but the carver

refused, saying it would look like a circle. The

heptadecagon is used as the shape of the pedestal

with a statue honoring Gauss in his home town of

Braunschweig.

Gauss on the 10 Mark note

AA

BBBB

CCCCCC

DDDD

FF

His diary that covered 20 years of work only

contained 19 pages. Gauss was a perfectionist. After

his death it was discovered that many discoveries

credited to others had first been worked on by Gauss years earlier. Much of his work was never published because he felt it wasn’t

finished yet.

His motto was "pauca sed matura" (few but ripe).

Eureka (num) = + +

Eureka (num) = + +

1 3 6 10 15

This entry from Gauss’ diary meant that every number

could be written as a sum of three or fewer triangular numbers.

Triangular Numbers: Number = Sum of 3 or f ewer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number = Sum of 3 or f ewer

1, 3, 6, 10, 15, 21, 28…

6 + 16 + 1 + 1

6 + 3

21 + 15 + 137

The Pythagorians believed “All is Number,” meaning that everything in the universe depended on numbers. They were also the first to teach that the Earth is a Sphere revolving around the sun.

Pythagoras is often

considered the first true

mathematician.

Many of Pythagoras’ beliefs reflect those of the Egyptians.

The Egyptian priests were very secretive.

The refusal to eat beans or wear

animal skins and striving for purity

were also characteristics of the

Egyptians.

a 2 + b 2 = c 2

The sum of the angles of a triangle is equal to two right angles or 180 degrees

The five regular solids

Venus as an evening star was the same planet as Venus as a morning star.

The abstract quantity of numbers. There is a big step from 2 ships + 2 ships = 4 ships, to the abstract result 2 + 2 = 4

Regular Solids

• Tetrahedron

• Cube

• Octahedron

• Dodecahedron

• Icosahedron

Regular Solids

• Measure the nets of the regular solids and find the surface area

One of the Pythagorian’s most important discoveries was that the diagonal of the square is longer than its sides. This showed that irrational numbers existed

(decimal numbers that never end).

a

b

c

a < cb < c

Joseph-Louis Legrange

France1736-1813

Started studying mathematics seriously at age 15;

appointed a professor of mathematics at age 17

Helped design the metric system,base 10 instead of base 12

Answered a 50-year old question concerning

constant perimeter with largest possible area

Given a constant perimeter, which shape will have the

greatest area?Each student (or group) needs • Several sheets of centimeter grid paper• Several pieces of yarn cut to the same

length (constant perimeter ≈ 30 cm)• Tape

Students will tape the string to the grid paperto make a polygon, then estimate the area ofthe polygon.

One of Legrange’s most significant discoveries in the area of Number

Theory:

Every positive integer can be expressed as a sum of four or

fewer square numbers.

1 x 1 = 1 2 x 2 = 4 3 x 3 = 9

1, 4, 9, 16, 25, 36…

■

■

■4 + 14 + 1 + 1

4 + 1 + 1 + 1

4 + 4

47 36 + 9 + 1 + 1

Mary Everest Boole

England1832-1916

1 2 3 4 5 6 7

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