History of Mathematics 473
Course Information
Instructor: Terry Millar (Professor of Mathematics)
Classes: Tuesday and Thursday, 11:00-12:15 Room 2425 Sterling Hall
Grading:
Classroom attendance
Final
Quizzes/Midterm
Term Paper
10%
20%
30%
40%
The qui

Term Paper
Title/Prcis Examples
Title: Japanese Temple Geometry Versus Western Mathematics
Precis: From 1639- 1854, Japan was in a state of national seclusion. In this Edo Period of isolation, native
mathematics took off. These ancient forms of mathematic

Problem Studies 57
Problem Studies
2.1 Regular Numbers
A number is said to be (sexagesimally) regular if its reciprocal has a ﬁnite
sexagesimal expansion (that is, a ﬁnite expansion when expressed as a radix
fraction for base 60). With the exception of a

The Law of The Lever
Continued
Postulate 1. Equal weights at equal distances are in equilibrium, and equal weights at
unequal distances are not in equilibrium
And what about the second half?
yxz M x z E2 ( y ; y x , y + z ; M , M )
What happens though if

Euclidean Geometry
Revisited
Alfred Tarski (1901-1983)
Material before parallel line section taken from 1999 JSL Tarskis System of Geometry article by Tarski and Givant
It took 2200 years, but eventually it became apparent to prominent mathematicians that

The Deep End
Archimedes
Buoyancy and Law of the Lever
Archimedes: 287 -212 B.C.
Born 287 B.C. Native of Syracuse on the island of Sicily
Archimedes: 287 -212 B.C.
His father was an astronomer
He studied at the University of Syracuse (probably did not play

For the Tarski equilateral triangle problem, you can use without proof any of the defined symbols and
lemmas that I proved or alluded to in class. For example:
Definition:
( xy < wz ) iff df
u1u2 B ( w, z , u1 ) ( xy zu1 ) B ( w, z , u2 ) ( wz zu2 ) B ( z

Oresme, Descartes, Galileo,
Thought experiments,
Observational and intervention experiments,
Rate of change
If a system has a continuous symmetry property, then there are corresponding quantities
whose values are conserved in time.
But first, we check in

An Introduction
Proof of Proposition I Book 1 of Euclids Elements
Using Tarksis Axioms rather than Euclids Postulates
Here is where we start:
Proposition 1. To construct an equilateral triangle on a straight line segment.
In the spirit of both Euclid and

More on Euclids Elements
And The Foundations
of
Modern Mathematics
Book II: Geometric Algebra
Proposition 1. If there are two straight lines, and one of them is cut into any number of
segments whatever, then the rectangle contained by the two straight lin

Archimedes and the Sphere
With an Infinitesimal Assist!
It is just possible that Archimedes, could he come to life long enough to take a
post-graduate course in mathematics and physics, would understand Einstein,
Bohr, Heisenberg, and Dirac better than th

Law of the Lever
Modern Application
A (More) Modern Application of the Center of Mass
How can it be that mathematics, being after all
a product of human thought which is
independent of experience, is so admirably
appropriate to the objects of reality?
Mak

Math 473 Assignment
Sherry Lixue Cheng
Galileos ExperimentsData pattern analysis
According to the assignment, the experimental set up is shown in Figure 1. The height h
of declined plane is relatively small to make the water clock easier to operate and le

Galileo Galilei (1564-1662)
Design Experiments
And the
Scientific Revolution
[Much of the material here comes from Michael Hobarts draft chapters]
Renaissance
~1300
~1700
A period from the 14th to the 17th century, considered the bridge between the Middle

Math 473 Assignment
Sherry Lixue Cheng
Galileos ExperimentsData pattern analysis
Introduction
According to the assignment, the experimental set up is shown in Figure 1. The height
(h) of declined plane is much smaller than the length of plank (L) to make

Infinitesimals
and
Intuition
Rebecca Vinsonhaler
Graduate Student C&I
A revised version of the term paper I wrote last year for this class (on the use of infinitesimals for calculus instruction) has been
accepted for publication.
Since you also have seen

Infinitesimals
Quarks
And other feats of the human imagination
(such as "Finnegan's Wake" by Joyce and Faust by Goethe)
Bertrand Russell when describing atoms:
It is chiefly through ideas derived from sight that physicists have been led to the
modern conc

473 Investigative Assignment
Quiz equivalent of 20 points
Due by Wednesday April 8 11pm
Please submit work to the Dropbox
Galileo faced many challenges while helping to invent/advance the scientific method. Measuring
techniques were not sufficient to accu