Date

CLASSWORK AND HOMEWORK
Work is due at the beginning of class
unless otherwise noted!

July 18  Mon 

July 19  Tues 
 Classwork
Linear equations: Egypt Rhind Papyrus, Babylon, China:
Egyptian Multiplication/Division
The origin of algebraic manipulation via
Linear Equations in One Unknown  Islamic Method worksheet from the
CD.
Chinese method of double false position of solving two linear equations
with two unknowns via Chinese Problems worksheet from the CD.
System of Three Linear Equations  The Chinese Solution
from Algebra Activities from Many Cultures
Multicultural Origin of the Quadratic Formula
worksheet from
Algebra Activities from Many Cultures
Brief history of the Pythagorean Theorem via web search:
site
and
site
MacTutor History
of Mathematics Archive
Scarecrow's Theorem
Slide 1
Slide 2
Copyright Slide
Cubic equations: Europe  leading to sqrt(1)
Solutions to the quintic
Maple demo and fictional account of Galois
Begin Wednesday's classwork.
 Homework for Wednesday
Daily Journal reflections for the first two days should be completed.
Your CD project topic must be approved by Dr. Sarah by
Wednesday.

July 20  Wed 
 Classwork
 What is geometry? Groups discuss and come back together.
 Brief history of early geometry knowledge including the
Babylonians, Egyptians, Greeks (Thales, Pythagoras, Plato, Euclid),
Chinese, and Africans.
Mention the Timeline for Geometry: Multicultural Highpoints
from Geometry Activities from Many Cultures
Skim LAV 6 section of the CD
on Origins of Length, Area, and Volume Measurement
Mention CD LAV 80 on Thales' Shadow Measurement Activity
Mention CD
Trig 80 and LAV 88 on Eratosthenes' Size of the Earth and
Trig 112 on AlBiruni's Calculation on the Size of the Earth
History of Euclid's elements including
Euclid's 5th postulate (prop 29 and later).
 Sum of the Angles in a Triangle:
Write out
Proposition 32 in modern language.
Discuss Euclid's historical proof,
paper folding,
and then an
Intro to Geometric Constructions
via a
construction in Sketchpad.
Dr. Sarah models the construction.
Discuss the history
(attributed to Pythagoras),
and compare and contrast the activities,
discussing the benefits and difficulties with using them in various classes.
Then the group goes to the computer lab to try the Sketchpad construction.
 Pythagorean Theorem:
Discuss the Yale tablet and Babylonian Pythagorean knowledge.
Discuss the history of
Euclid Book 1 Proposition 47 and of it's importance in measurement.
Discuss Sketchpad demonstrations of the Pythagorean Theorem. From
Sketchpad, under File/open, go to
Desktop/205Math(yourcomputersnumber)/Applications(MacOS9)/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp
Go through Behold Pythagoras! and Puzzled Pythagoras.
Return to the classroom.
Highlight the other proof from the video
(Euclid's Pythagoras), and then Dr. Sarah's models the construction in
Sketchpad.
Mention CD activities
LAV 124 Pythagorean Theorem,
LAV 130 Practical Pythagorean Theorem,
Geom 103 Pythagorean Project
Hand out A Chinese Proof of the Theorem from
Geometry Activities from Many Cultures
in order to complement the Sketchpad Behold Pythagoras! activity
Compare and contrast the methods used in the classroom.
 NonEuclidean Geometry:
Dynamic Geometry activities on the sphere and hyperbolic Poincare disk
Walter Fendt's Java Applet
and the sum of the angles and the Pythagorean Theorem
Escher worksheet
Sketchpad
Hyperbolic Sum of Angles
Sketchpad
Hyperbolic Pythagorean Theorem
Mention built in hyperbolic Sketchpad exploration and
Brad Findell's Elliptic/Spherical Toolkit for Sketchpad
Why Study
Hyperbolic Geometry? and a brief
history of
nonEuclidean geometry.
Crochet Model of Hyperbolic
Geometry
Hand out Explorers of NonEuclidean Geometry from
Geometry Activities from Many Cultures
Mention CD Trig 151 on Spherical Trig
Read through the
Shape of the Universe and discuss
 Return to the computer lab. History of modern geometry
via web searches. Return to the classroom.
A brief history of
geometry education.
 Brief history of the connections and
differences between algebra and geometry
The Proof video
Mention the teacher's guide available at
NOVA Online
Powers
of twelve activity
 Homework for Thursday
Complete the CD assignment and work on the Daily Journal.

July 21  Thur 
 Classwork
 Finish up classwork from Wednesday
 CD presentations
Sharon Poly 50 Finding Cube Roots
Gina Poly 33 Deriving the Quadratic Formula
Emogene Trig 12 Angle Degree and Radian Measure
Suzanne Geom 7 Checkerboard Challenge
Joy Lav 33 Sticks, Stones, and Ropes
Bob NegNums 55 AlKhwarizmi's Negative Numbers
Jeremy Lav 118 Euclid's Geometric Algebra
Amelie ExpLog 36 Manhattan Purchase
Cam Lav 71 Housing
Jeanne NegNums 90 Excuse Me Do You Have the Time?
Danielle Lav 111 Golden Mean
 Ben Franklin's Will
 Begin calculus:
Discussion based on The Paradoxes of Zeno from
From Agnesi to Zeno
Quadrature of the lune
 Archimedes:
Archimedes and pi via inscribed and circumscribed polygons.
Hand out the
Hypatia
worksheet
Examine the related NOVA website applet
Archimedes finding the area of a parabola in terms of the area of a
triangle and the quadrature of a parabola
Archimedes computation of the area of a sphere as four
times the length of the great circle via oranges
Archimedes and the
volume of a sphere.
Read and discuss
Measuring Volumes
 Applications of series:
history of the approximation of Pi
and the number of known digits of Pi.
Apu and pi in Maple, and search for the world record on
the number of digits. Discuss Bailey and Borwein's series.
 Calculus: Barrow, Newton, and Leibniz
 The spread of calculus: Agnesi and the
witch of Agnesi
Analytical Institutions
Witch. Handout worksheet From Agnesi to Zeno
 Rigor in calculus and modern analysis
 Homework for Friday
Complete the Daily Journal.

July 22  Fri 
 Classwork
 Finish calculus
 Issues in current research on
history of math and ethnomathematics and web searches
 CD presentation reflections
 Look at textbooks
 Melt evaluations
 Reflection assessment
 Hand out main web page
 Homework for Saturday July 30th Work on the final project.

July 30  Sat 
 Final project due as a wordprocessed document or a PDF file,
sent as an attachment in an email to greenwaldsj@appstate.edu.
 Final projects as word files:
Danielle Fractals
Emogene Plato's Dialogue Meno
Bob Historical Pi
Jeremy Just How Big is the Earth Anyway?
Gina Patterns of Operations for Integers
Cam Aztec Mathematics
Jeanne Shang Numerals and Counting Boards
