Linda Salgado Troup Middle School Math Blast From the Past Linda Salgado Troup 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

www.IKeepBookmarks.com account: SalgadoL no password needed List of many websites on mathematicians

Rene Descartes France 1596-1650 Co-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

Archimedes Syracuse (then part of Greece) 287-212 BC

Discovered how to calculate the volume 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

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 Italian postage stamp honoring Archimedes May 2, 1983 Scott Catalogue Number 1559

Archimedes water screw

(Archimedes the geometer). A 1740 engraving of Archimedes planning the defenses of Syracuse. The Greek writing on his cap is                      (Archimedes the geometer).

Painted by Giulio Parigi (1571-1635) in the years 1599-1600. 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.

war gadgets may have worked. Archimedes designed many tools for defending Syracuse from invasion. This is a model of how one of Archimedes war gadgets may have worked.

Burning Mirror Archimedes 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 from Mechanics Magazine London, 1824 Give me a place to stand and I will move the earth Engraving from Mechanics Magazine London, 1824

The Law of the Lever w2 w1 d1 d2 fulcrum w1 x d1 = w2 x d2

w1 x d1 = w2 x d2 w1 x 5 = 400 x 5 w1 = 400 w1 x d1 = w2 x d2 400 pounds 5 feet ? w1 x d1 = w2 x d2 w1 x 5 = 400 x 5 w1 = 400 2 feet 8 feet ? 400 pounds w1 x d1 = w2 x d2 w1 x 8 = 400 x 2 w1 = 100

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 (1706-1790) 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 discovered electricity, bifocal eye glasses, the odometer and a wood burning stove, among many other things. Ben Franklin sitting on a bench. Artwork on the campus of the University of Pennsylvania.

Magic Squares Arrange the numbers 1-9, using each number only once. All rows, columns and diagonals must add to the same number

8 5 3 2 9 7 6 1 4 = 16 = 18 MEAN = 15 = 11 Magic Squares Arrange the numbers 1-9, using each number only once. All rows, columns and diagonals must add to the same number

Multiply each number by some integer…is it still a magic square? Magic Squares 15 = 15 Multiply each number by some integer…is it still a magic square? 8 1 6 3 5 7 4 9 2 15 15 15 15 Correct Answer

Magic Squares Arrange the numbers 15-23, using each number only once. All rows, columns and diagonals must add to the same number

each row, column, & diagonal 15 16 17 18 19 20 21 22 23 171 171 ÷ 3 = 57 each row, column, & diagonal

Carl Friedrich Gauss Germany 1777-1855 5050 1 + 2 + 3 + … + 98 + 99 + 100 = 5050

English German Spanish Danish Latin Greek French 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. English German Spanish Danish Latin Greek French

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

"Normal" Curve used in statistics B C D F

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

Eureka (num) = + +

Triangular Numbers 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. Eureka (num) = + +

Triangular Numbers

1, 3, 6, 10, 15, 21, 28… 37 21 + 15 + 1    6 + 1 6 + 1 + 1 6 + 3 

Pythagoras Greece 560-480 BC

Pythagoras is often considered the first true mathematician. 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.

Many of Pythagoras’ beliefs reflect those of the Egyptians 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.

Pythagorean Theorem a 2 + b 2 = c 2

The sum of the angles of a triangle is equal to two right angles or 180 degrees Venus as an evening star was the same planet as Venus as a morning star. The five regular solids 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 < c b < c c 2 a 3.1415927... b

Joseph-Louis Legrange France 1736-1813

Started studying mathematics. seriously at age 15; appointed a 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 paper to make a polygon, then estimate the area of the 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… ■ 47 36 + 9 + 1 + 1 ■ 4 + 1 4 + 1 + 1 4 + 1 + 1 + 1 4 + 4 ■

Mary Everest Boole England 1832-1916 4 5 6 7 1 2 3 4 5 6 7

Line Designs Or String Art www.Mathcats.com/crafts/stringart.html