EMAT 6600
Problem Solving in Mathematics
Spring, 2008
On line course evaluation after May 23
This is the web site page devoted to EMAT 6600 Problem Solving in Mathematics, at the University of Georgia, as led by Jim Wilson.
Last modified on January 26, 2008
Send e-mail to jwilson@uga.edu
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EMAT 6600 Documentation
- EMAT 6600 Syllabus - General information about the
objectives and operation of the course.
- Introductory
Remarks
- Resources
PAPERS:
- Synthesis
of Research on Problem Solving. This paper was published as
Chapter 4 in
Wilson, P. S. (Ed.) (1993). Research Ideas for the
Classroom: High School
Mathematics. New
York: MacMillan.
The book was part of the National Council of Teacher of
Mathematics Research Interpretation Project, directed by Sigrid Wagner.
The bibliographic reference for the published version is
Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993).
Mathematical problem solving. In P. S. Wilson (Ed.), Research Ideas for the
Classroom: High School
Mathematics (pp.
57-78). New York: MacMillan.
- Squares.
What is the ratio of areas of the two squares?
This is a discussion of some exploration
and extensions of this problem. - Roots 2 and 5. This paper
examines sets of equations that have graphs crossing the x-axis only at 2
and 5. For a preview on one family of such graphs, click here.
- Problem
Solving with Heron's Formula. This is a paper on the development and demonstration of
Heron's formula for the area of a triangle given the lengths of its three
sides. Problems and explorations are included for using Heron's formula.
- An
Investigation with Parametric Equations. This paper examines the
movement of triangles when one vertex is moved along the x-asis and
another is moved along the y-axis. We trace trace the movement of the
third vertex.
- Extended Concurrencies of the
Triangle
PROBLEMS:
Project InterMath
Project InterMath has a web site with many
investigations deemed appropriate for Middle School mathematics teachers. I
believe secondary mathematics teachers may find some challenges here as well.
Please access the site: Project INTERMATH
Environment Problems
- Volume
of an Irregular Solid
- The Three Point Problem from Geology
- Volume of a curved trench, Trapezoid
Cross-section
- Distance survey
Geometry Problems
- 100 degree isosceles triangle
- A Cyclic Quadrilateral
- A Mean Problem
- Angle Bisector of two line
non-intersecting line segments
- Angle of View
- Arc
Length equal to a given segment
- Areas of a Rectangle
- Bisector
of an angle of a triangle
- Bisectors Problem in 120 degree Obtuse
Triangle
- Brahmagupta's Formula
- Carl's Cone
- Checkerboard Problems
- Circle Theorems Review
- Circles
of Apollonius for a Triangle ABC
- Circular Window
- Color a Circle
- Coloring Circles
- Concurrency Theorems
- Cone Half Full
- Count the Triangles -- I
- Count the Triangles -- II
- Count the Triangles -- III
- Cutting the Cake
- Equilateral Triangle Altitude
Theorem
- Equiperimetric Areas
- Excircle Problems
- Find Inscribed Square for Given
Triangle
- Find Inscribed Rectangle with Maximum
Area for Given Triangle
- FlowingStream
- Fly and Spider
- Folding
a sheet of paper into equal areas
- Four dogs
- Half
the Area of a Triangle: A Line Parallel to a Side
- Half the Area of a Triangle: A line
Through a Point on the Side
- Heron's
Formula
- Incircle Problems
- Inequality in a triangle
- Inscribed Equilateral Triangle in a Square – Construction
- Inscribed Equilateral Triangle in a
Square –
Problem
- Inscribed Quadrilateral
- Inscribed
Triangle
- Island Treasure
- Isosceles
Right Triangles--Path of the Mid-Point
- Isosceles
Right Triangles With a Common Vertex
- Isosceles trapezoid
- Isosceles Trapezoid -- Equal
areas
- Kite
- Lines of Symmetry in a Polygon
- Locus of intersection of two secants
- Locus Problems
- Maximum Quadrilateral
- Medians of a Triangle
- Menelaus's Theorem
- Mid-Segment Theorem
- Networks
of Minimal Length
- Notch
for Felling a Tree
- Obtuse Triangle Relationship
- Pairs
of Segments with the Same Sum of Lengths
- Parallelogram with Integer
Sides and Integer Diagonals
- Partition Square into Acute Triangles
- Perfect Triangles
- Pappus Areas
- Perpendicular
Chords in a Circle
- Points closer to the Centroid than
the Sides
- Polya's Problem 2.35.1
- Ptolemy's Theorem
- Pyramids in a Prism
- Quadrilateral Inscribed in a
Semicircle
- Quadrilateral
with Maximum area
- Quadrilateral
with Squares on the Sides
- Ratio Sums from Orthocenter
- Ratio
on a line segment -- Something Golden
- Ratio:
Segments cut off by an angle bisector to the adjacent sides
- Right Triangle Constructions
- Right
Triangle Relationships
- Right Triangle with perimeter 60, altitude
to hypotenuse 12
- Rotating Triangle
- Spheres
- Square Inscribed along a base of any
Triangle
- Squares Inscribed in a Right Triangle
- Squares
on the Sides of a Parallelogram
- Sum
of Ratios
- Tangent and Secant Problem
- Tangent Lines Common to Two Given Circles
- The Problem of Apollonius
- Three Circles
Problem
- Trapezoid Inscribed in a Semicircle
- Triangle
areas/Steinhaus
- Triangle areas/Triangle Built on Outside of
a Given Triangle
- Triangle
Area and the Circumcircle
- Triangle Constructions
- Triangle Loci
- Triangle Mid-Segment Theorem
- Triangle/Square
- Triangles
and Squares
- Triangles with Integer Area and Integer
Sides
- Two
triangle problems
- Two Squares
- Volume
of Holes Left by Tree Spade
Algebra Problems
Solve by iteration. - 7-11
Problem
- A
Tangled Tale Problem
- Average Rate
- Big Tires
- Calculator sequence
- Candy
Problem
- Comparision of Two Radical
Expressions
- Equiperimetric Areas
- Heart to Bell
- Jordan's
Inequality
- Linear
functions tangent to their product function
- Maximum Volume of a Cone
- McNuggets
- Minimal
area triangle
- Phonograph
groove
- s(s-c)
= (s-a)(s-b)
- Simultaneous Quadratics
- Square Root Equation
- Sum
of Unit Fractions
- Volume of a Frustum
Solve by iteration
Conversion
Problems
Cryptarhythm Problems
"Mean" Problems
- AM-GM
Problems
- Arithmetic
Mean -- Geometric Mean Inequality
- Areas in square of sides a+b
- Area
of a Sector of a Circle
- Average Rate
- Box
Problem
- Comparing
Segments in two circles
- Comparison of altitude and median
in a right triangle
- Equiperimetric Areas
- Harmonic
Mean Problems
- Maximum
area -- rectangle
- Maximum
area -- triangle
- Maximum and Minimum
of (x/(1+x^2))
- Maximum of f(x) = (1-x)(1+x)(1+x)
- Minimum
of x + 1/x
- Minimum Surface area of a can
of fixed volume
- Phonograph
groove
Trigonometry
Problems
Mixture of all
- 7-11
Problem
- Area of Texas
- A sequence from Eudoxus
- A
Will to be Interpreted
- Area Golfing Greens
- Arithmetic Mean Sequence
- Bottles
and Cans
- Census Taker Problem
- Change
for a Dollar
- Coins
- Compare Radicals
- Distance to Nearest Road
- Fractions
- Friday
13
- FlowingStream
- Four Number Challenge Problem
- Grass
Consumption by Oxen
- How Wide is the Alley?
- Ladder and Box
- Magic
Square
- Maximum Volume of a Cone
- Mirror
Image
- Oil Tank Problems
- Rational or Irrational
- Square Root of 2
- The
Salesperson's Journey
- Triangular
Numbers
- Where is the store?
Final Project
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