Transcript Blast From The Past - Troup Independent School District

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 SchmandtBesserat
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
X
y
z
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.
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
2
x
Developed Exponential system of writing
large numbers
Discovered the Law of the Lever
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
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 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 15991600.
Give me a place to stand and I will move the earth
Engraving from
Mechanics Magazine
London, 1824
The Law of the Lever
w1
d1
d2
w2
fulcrum
w1 x d1 = w2 x d2
400 pounds
?
5 feet
w1 x d1 = w2 x d2
w1 x 5 = 400 x 5
w1 = 400
5 feet
400 pounds
?
8 feet
w1 x d1 = w2 x d2
w1 x 8 = 400 x 2
w1 = 100
2 feet
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 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.
Arrange the numbers 1-9, using each number
only once. All rows, columns and diagonals must
add to the same number
5
9
1
3
7
4
= 16
= 18
= 11
Arrange the numbers 1-9, using each number
only once. All rows, columns and diagonals
must add to the same number
MEAN = 15
8
2
6
15
Multiply
each
number by
some
integer…is it
still a magic
square?
8
1
6
= 15
3
4
5
9
7
2
= 15
15
15
15
15
= 15
Correct Answer
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 = 57
each row, column, & diagonal
Benjamin Franklin’s Numbers
52
14
53
11
55
9
50
16
1.
2.
3.
4.
5.
6.
7.
8.
61
3
60
6
58
8
63
1
4
62
5
59
7
57
2
64
13
51
12
54
10
56
15
49
20
46
21
43
23
41
18
48
29
35
28
38
26
40
31
33
36
30
37
27
39
25
34
32
45
19
44
22
42
24
47
17
Find the sum of any row:
Find the sum of any column:
Find the sum of the first four numbers of any row:
Find the sum of the last four numbers of any row:
Find the sum of the first four numbers of any column:
Find the sum of the last four numbers of any column:
Find the sum of the four corners:
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.
52
14
53
11
55
9
50
16
61
3
60
6
58
8
63
1
4
62
5
59
7
57
2
64
13
51
12
54
10
56
15
49
20
46
21
43
23
41
18
48
29
35
28
38
26
40
31
33
36
30
37
27
39
25
34
32
45
19
44
22
42
24
47
17
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
F
F
D
D
D
D
C
C
C
C
C
C
B
B
B
B
A
A
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) =
+
+
1
3
Eureka (num) =
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:
1, 3, 6, 10, 15, 21, 28…
Number = Sum of 3 or fewer 
1
2
3
4
5
6
7
8
9
10
11
12



6+1
6+1+1
6+3

Number = Sum of 3 or fewer 
37
21 + 15 + 1
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.
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.
a2+b2=c2
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).
c
a
b
a<c
b<c
Joseph-Louis Legrange
France
1736-1813
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 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.
1x1=1
2x2=4
3x3=9
Square Numbers:
1, 4, 9, 16, 25, 36…
Number = Sum of 4 or less squares
■
1
2
3
■
4
4+1
5
4+1+1
6
7 4+1+1+1
4+4
8
■
9
10
Number = Sum of 4 or less squares
47
36 + 9 + 1 + 1
Mary Everest Boole
England
1832-1916
1
2
3
4
5
6
7
1 2 3 4 5 6
7
Line Designs
Or
String Art
www.Mathcats.com/crafts/stringart.html