Linda Salgado Troup Middle School. Mathematicians Are People, Too (Volumes 1 and 2) Reimer & Reimer,...
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Transcript of Linda Salgado Troup Middle School. Mathematicians Are People, Too (Volumes 1 and 2) Reimer & 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
www.IKeepBookmarks.com
account: SalgadoL
no password needed
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
1234567
Line DesignsOr
String Art
www.Mathcats.com/crafts/stringart.html