CLASSWORK AND HOMEWORK
Work is due at the beginning of class
unless otherwise noted!
|July 18 - Mon
|July 19 - Tues
Linear equations: Egypt Rhind Papyrus, Babylon, China:
The origin of algebraic manipulation via
Linear Equations in One Unknown - Islamic Method worksheet from the
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
Algebra Activities from Many Cultures
Brief history of the Pythagorean Theorem via web search:
of Mathematics Archive
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
|July 20 - Wed
- 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
Trig 80 and LAV 88 on Eratosthenes' Size of the Earth and
Trig 112 on Al-Biruni'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:
Proposition 32 in modern language.
Discuss Euclid's historical proof,
and then an
Intro to Geometric Constructions
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
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
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.
- Non-Euclidean 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
Hyperbolic Sum of Angles
Hyperbolic Pythagorean Theorem
Mention built in hyperbolic Sketchpad exploration and
Brad Findell's Elliptic/Spherical Toolkit for Sketchpad
Hyperbolic Geometry? and a brief
Crochet Model of Hyperbolic
Hand out Explorers of Non-Euclidean 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
- Brief history of the connections and
differences between algebra and geometry
The Proof video
Mention the teacher's guide available at
of twelve activity
- Homework for Thursday
Complete the CD assignment and work on the Daily Journal.
|July 21 - Thur
- 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 Al-Khwarizmi'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 and pi via inscribed and circumscribed polygons.
Hand out the
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
- 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
Witch. Handout worksheet From Agnesi to Zeno
- Rigor in calculus and modern analysis
- Homework for Friday
Complete the Daily Journal.
|July 22 - Fri
- 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 word-processed document or a PDF file,
sent as an attachment in an email to firstname.lastname@example.org.
- Final projects as word files:
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