The Mad
Scientists
Present:
“Scientific and Mathematical
Inventions”
A Web Quest
The Chicken and the Egg
and the Caveman and
the Space Station!
Which came first, the chicken or the egg? The same brainteaser could
probably be applied to math and technology. Did the math come out of
the technology or are they in fact inseparable. In the movie 2001: A
Space Odyssey, there is a famous opening scene that depicts our
Neolithic ancestors using rocks and sticks as tools and then abruptly
transitions to space aged humans of the future living in space colonies.
The point being that when the first human picked up a rock and used it
as a tool the future was determined. Unfortunately, mankind had to
wait 50,000 years until the Greeks, Archimedes in particular, realized
that there was a direct relationship between the size of the rock, the
length of the arm, and the force of the blow. The mind of man had
managed, through pure thought, to harness the forces of the universe
for his own purpose. Archimedes, in mathematical terms, could now in
a fundamental way predict the outcome of an event before it happened.
Archimedes laid down the foundation for the most powerful
mathematic tool known to mankind – the Calculus. Unfortunately
again, mankind had to wait another 2,500 years for Newton and
Leibnitz to work out all the details. Math and technology are
interrelated; one describes the other and one predicts the other. All
technologies have mathematical roots: computers, the internet,
telecommunications; and all math has practical application - one is the
language of the other.
The Web Quest
1. Read each question carefully
2. Visit each web site and
browse the suggested pages
3. Answer the questions
Pythagorus and Euclid
“It’s all Greek to me”
Application of Pythagorean Theorum to
Einstein’s theory of special relativity
Pythagorus
Question 1.
Throughout 8th grade math you learn many concepts related to
geometry. One in particular is the Pythagorean Theorem, 1st
proven by Pythagoras and his followers. In what subject were
Pythagoreans most interested?
http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
Question 2.
Euclid established or invented many of the rules we all use in
Geometry today. Euclid wanted to prove things were true by using
what?
http://www.historyforkids.org/learn/greeks/science/math/euclid.htm
Example of Euclidian geometric shape
Question 3.
Pi is an important mathematical invention for understanding circles.
Mathematicians in what Empire are credited for figuring out or “inventing” pi?
http://www.historyforkids.org/scienceforkids/math/geometry/pi.htm
Its Pi or Nothing
Question 4.
The Indian mathematicians’ biggest invention was the use
of the number zero as what?
http://www.historyforkids.org/learn/india/science/math.htm
“Mathematicians have nothing to shout about”
New to Numbers
and Shapes
Question 5.
What is the name of the sequence in which the next number
in the series is generated by adding the two previous
numbers: (1,1,2,3,5,8,13,21,34,55)?
http://www.fortunecity.com/emachines/e11/86/natsums.html
Question 6.
In the 17th century, who showed that if two bodies attract each other with
force that was proportional to the square of the distance between them, then
the resulting motion of body relative to the other would be a precise
mathematical curve called a conic section (that is, a circle, ellipse, parabola
or hyperbola)? Although this person was not the first person to suggest that
the inverse square law of force was responsible for the motion of the planets,
his great triumph was to provide a mathematical proof of the consequences
of such a law.
http://www.fortunecity.com/emachines/e11/86/solarsys.html#Newton
Cotton Gins and Flying Buttresses
Practical Applications
Question 7.
What is a buttress?
Who invented it?
What function does it serve?
http://www.historyforkids.org/learn/architecture/buttress.htm
Question 8.
What are some famous locations where “flying buttresses” are
used?
http://www.historyforkids.org/learn/architecture/flyingbuttress.htm
Question 9.
Relating to mathematics … a size X buttress can support a size
Y wall. Find the ration of X and Y? Go to the following site for
useful information.
http://www.mae.ufl.edu/~uhk/STATICS.html
Question 10.
What is a cotton gin?
Who invented it?
What function does it serve?
What was the unfortunate side-effect of its
invention?
http://www.eliwhitney.org/cotton.htm
Question 11.
Relating to mathematics … how much more
cotton could be harvested by using a cotton
gin?
http://edtech.kennesaw.edu/web/inventor.html
Geometry and Perspective
Question 12.
In which masterpiece did Leonardo Da Vinci use a complex formula based
on the relationship 12:6:4:3? (Note: The entire piece measures 6 by 12
units. The wall in the back is equal to 4 units. The windows are 3 units and
the recession of the tapestries on the side walls is 12:6:4:3.)
http://www.facstaff.bucknell.edu/udaepp/090/w2/Magee.htm
Question 13.
What book written by Euclid became the basis of geometry?
It was based on the geometry of the Greeks. After it was
written, it became the basis of geometry itself. People used
the information in the volumes to do a lot of practical things,
such as making accurate measurements. For example,
building a house, or a computer would be very hard without
geometry, as you would have to measure the shapes of the
computer. People use geometry to calculate numbers,
measure shape, width, and height.
http://derrel.net/math/euclid/euclid_inventions.htm
Jacquard Loom
In 1911, four companies, including the Herman
Hollerith Tabulating Machine Company combined to
form a larger company known as the International
Business Machines Corporation (IBM). Herman
Hollerith had devised a way to store information on
punched cards. Hollerith borrowed the idea for
punched cards from a weaving machine, the
Jacquard Loom, which used a card system for
ordering weaving operations on a silk loom. A hole
in the card was a signal for the loom to perform an
operation. In other words the card represented a
machine code. The machine code, a simple yes-no,
on-off concept is transcribed mathematically as 0
for off, or no, and a 1 for on or yes. This
mathematic formulation has brought us personal
computers (PC’s), supercomputers, the digital
revolution, and the internet.
Ones and
Zeros
Punched card
Question 14.
Review the following web site. Who, like Hollerith, planned to
use punched cards to control an analytical engine?
http://www.cs.uiowa.edu/~jones/cards/history.html
Question 15.
Review the following web site. What decimal number
does the binary number 101101 correspond to: 3, 4, 17,
45, 53?
http://php.about.com/od/programingglossary/qt/binary.htm
BONUS
In the movie 2001: A Space Odyssey,
the talking supercomputer is called
HAL. Move each letter forward one in
the alphabet and see what you get.