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

2. 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

3. 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

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

5. Rene Descartes France 1596-1650
Co-Founder of
Analytic Geometry

6. 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

7. Archimedes
Syracuse
(then part of Greece) BC

8. 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

9. 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

10. Archimedes water screw

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

12. 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 ( ) in the years

13. 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.

17. Burning Mirror
Archimedes used mirrors to reflect and intensify the sun, causing the ships to catch on fire.

18. Wall painting from the Stanzino delle Matematiche in the Galleria degli Uffizi
(Florence, Italy). Painted by Giulio Parigi ( ) in the years

19. Engraving from Mechanics Magazine London, 1824
Give me a place to stand and I will move the earth
Engraving from Mechanics Magazine London, 1824

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

21. 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

22. 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.

23. The death of Archimedes depicted on a Roman floor mosaic

24. Benjamin Franklin
( )
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 As a civic leader, he initiated a number of new programs in Philadelphia, including a fire company, fire insurance, a library, and a university.

25. 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.

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

28. 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

29. 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
Correct Answer

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

31. each row, column, & diagonal15 16 17 18 19 20 21 22 23
171
171 ÷ 3 = 57
each row, column, & diagonal

34. Carl Friedrich Gauss Germany 1777-1855 5050
… =
5050

35. 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

37. 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.

38. Gauss on the 10 Mark note

39. "Normal" Curve used in statisticsB C D F

40. 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.

41. Eureka (num) =

42. Triangular Numbers
This entry from Gauss’ diary meant that every number could be written as a sum of three or fewer triangular numbers.
Eureka (num) =

43. Triangular Numbers

44. 1, 3, 6, 10, 15, 21, 28… 37   
6 + 1
6 + 3 

45. Pythagoras
Greece BC

46. 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.

47. 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.

48. Pythagorean Theorem
a 2 + b 2 = c 2

49. 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 = 4

50. Regular Solids
Tetrahedron
Cube
Octahedron
Dodecahedron
Icosahedron

51. Regular Solids
Measure the nets of the regular solids and find the surface area

52. 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 b

53. Joseph-Louis Legrange
France

54. 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

55. 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.

57. 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 = x 2 = x 3 = 9

58. 1, 4, 9, 16, 25, 36… ■ ■
4 + 1
4 + 4 ■

59. Mary Everest Boole England 1832-19164 5 6 7

60. Line Designs Or
String Art