Problem Solving in Mathematics

Spring 2013

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This course will not be offered again until Spring 2015 semester.

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Last modified on April 16, 2013.     Send e-mail to Jwilson@uga.edu. Back to Jim Wilson's Home Page

EMAT 4600/6600 Documentation

EMAT 4600/6600 Syllabus   - General information about the objectives and operation of the course.

Introductory Remarks

Resources

EMAT 4600/6600 Class Members, Spring 2013.

Click HERE to send an e-mail to the entire class.
Go to the Class list for individual e-mail addresses.

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.(SP '13)  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

Recently Added

 

Three-Color Circle Patterns Sp'13

Color a Circle Sp'13

Quotient of Two Linear Functions Sp'13

Powers of the Golden Ratio Sp'13

Trisection of the Area of a Triangle Sp'13

Division Problem with 8 in the Quotient Sp'13

Area Bounded by Quarter Circle Arcs in a Square Sp'13
Patterns in a Whole Number Array  Sp'13

Segment Parallel to Bases of a Trapezoid through Intersection of Diagonals Sp'13

Multiple Solutions Sp'13
Arctan Sum Sp'13

Rational Equation Sp'13

Area of a Segment of a Circle Sp'13

Overlap Two Circles Sp'13

Minimum Integer when Dividing a 5-Digit Whole number by the Sum of its Digits Sp'13

Maximum Volume of a Cylinder Inscribed in a Sphere Sp'13

Check Cashing Problem Sp'13

 

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 Sp'13

 

Environment Problems

       

Distance survey   Sp'13

Volume of a curved trench, Trapezoid Cross-section

Volume of an Irregular Solid

The Three Point Problem from Geology  

 

   Geometry Problems

20-30-130 Triangle

100 degree isosceles triangle

Angle Bisector of two line non-intersecting line segments Sp'13

Angle of View

Arc Length equal to a given segment

Arctan Sum Sp'13

Area of a Segment of a Circle Sp'13

Area and Side of a Rhombus Given its Diagonals 

Areas of a Rectangle

Areas of Lunes I Sp'13

Areas of Lunes II Sp'13

Areas of Lunes III

Bisector of an angle of a triangle

Bisectors Problem in 120 degree Obtuse Triangle Sp'13

Bouncing Barney Sp'13

Brahmagupta's Formula

 Carl's Cone Sp'13

Ceva's Theorem Sp'13

Checkerboard Problems  

Circle Theorems Review Sp'13

Circles of Apollonius for a Triangle ABC  

Circular Window  

Concurrency Theorems Sp'13

Cone Half Full Sp'13

Count the Triangles -- I   Sp'13

Count the Triangles -- II   Sp'13

Count the Triangles -- III   Sp'13

Construct Equilateral Triangle with Vertices on Three Given Parallel Lines Sp'13

Cutting the Cake Sp'13

Cyclic Quadrilateral

Dissect a Square into a Set of Acute Triangles Sp'13

Dissect a Triangle a form a Square

Divide a Circle into Five Equal Areas Sp'13

Equilateral Triangle Altitude Theorem

Equiperimetric Areas Sp'13

Excircle Problems  

Find Inscribed Square for Given Triangle  

Find Inscribed Rectangle with Maximum Area for Given Triangle

FlowingStream  Sp'13

Fly and Spider  

Folding a sheet of paper into equal areas  Sp'13

Four dogs

Goat Tethered in a Field

Goat Tethered to the Edge of a Square Field Sp'13

Golden Ratio Calipers

Golden Ratio Construction Sp'13

Golden Triangle  (same as Sublime Triangle) Sp'13

Half the Area of a Triangle: A Line Parallel to a Side Sp'13

Half the Area of a Triangle: A line Through a Point on the Side Sp'13

Heron's Formula Sp'13

Heron's Formula: Geometric Proof  Sp'13

Incircle Problems  

Inequality in a triangle

Inscribed Equilateral Triangle in a Square -- Construction  

Inscribed Equilateral Triangle in a Square -- Problem  

Inscribed Quadrilateral

Inscribed Trapezoids 

Inscribed Triangle in a given triangle  

Island Treasure  Sp'13 

Isosceles Right Triangles--Path of the Mid-Point

Isosceles Right Triangles With a Common Vertex

Kite  

Lines of Symmetry in a Polygon

Lines Parallel to the Bases of a Trapezoid -- HM-GM-AM-RMS Inequalities

Lighthouse Problem: Three lighthouses

Locus of intersection of two secants

Locus Problems  

Maximum Quadrilateral  

Medians of a Triangle  

Menelaus's Theorem

Minimum Path Sp'13

Networks of Minimal Length Sp'13

Notch for Felling a Tree

Obtuse Triangle Relationship

Octagon Construction and Formulas Sp'13

Orthogonal Parabolas

Overlap Two Circles Sp'13

Pairs of Segments with the Same Sum of Lengths

Paper Knot Pentagon Sp'13

Parallelogram with Integer Sides and Integer Diagonals

Parallel Chords

Partition Square into Acute Triangles Sp'13 

Perfect Triangles Sp'13

Patterns Constructed in Circles Sp'13

Patterns of Circles and Squares; Comparision of Areas 

Pappus Areas Sp'13

Path Problems Sp'13

Perpendicular Chords in a Circle

Points closer to the Centroid than the Sides

Polya's Problem 2.35.1 Sp'13

Problem of Apollonius

Projections: Homothetic Similarity

 Ptolemy's Theorem Sp'13

 Pyramids in a Prism

Quadrilateral Determined by Intersecting Orthogonal Parabolas

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   Sp'13

Ratio: Segments cut off by an angle bisector to the adjacent sides   

Right Triangle Constructions

Right Triangle Relationships Sp'13

 Right Triangle with perimeter 60, altitude to hypotenuse 12

 Rotating Triangle

Septagon  Sp'13

 Spheres

 Square Inscribed along a base of any Triangle  

 Squares Inscribed in a Right Triangle

Square Inscribed in a Semicircle -- find a ratio

 Squares on the Sides of a Parallelogram  

 Sum of Ratios

Sublime Triangle(Same as Golden Triangle) Sp'13

Tangent and Secant Problem

Tangent Lines Common to Two Given Circles

The Problem of Apollonius

Three Adjacent Squares (THIS IS A GEOMETRY PROBLEM -- not trigonometry) Sp'13

Three Circles Problem

Three Intersecting Circles

Trapezoid Divided into Equal Areas by a Line Parallel to the Base

Trapezoid with Parallel through the Intersection of the Diagonals Sp'13

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 Inscribed in a Rectangle

 Triangle Loci

 Triangle Mid-Segment Theorem     Sp'13

 Triangles and Squares  

Triangles with Integer Area and Integer Sides

Triangle with Median Equal to the Base and Sides of Length 1 and 2

Trirectangular Vertex Problem

Two triangle problems  

Trisection of the Area of a Triangle Sp'13

Two Squares

Volume of Holes Left by Tree Spade Sp'13 

Algebra Problems

 

7-11 Problem Sp'13

A Tangled Tale Problem

Area bounded by Quarter-Circles in a Square Sp'13

Big Tires Sp'13

Calculator sequence

Candy ProblemSp'13

Check Cashing Problem Sp'13      

Combining Percentages Sp'13

Combining Rates Sp'13

Comparision of Two Radical Expressions

Equiperimetric Areas Sp'13

Exponents Equation

Golden Ratio and Fibonacci Sequence I Sp'13

Heart to Bell

Iron Ball Floating in Vat of Mercury

Jordan's Inequality Sp'13

Linear functions tangent to their product function   

Maximum Volume of a Cone Sp'13

McNuggets  Sp'13

Minimal area triangle

Orthogonal Parabolas  

Phonograph groove

Powers of the Golden Ratio Sp'13

Pythagorean Triples

Quotient of Two Linear Functions Sp'13

Rational Equation

s(s-c) = (s-a)(s-b)   Sp'13

 Simultaneous Quadratics  

 Square Root Equation  

  Sum of Unit Fractions

Three Mile Roadway -- Two line segments and an arc Sp'13

Two Stamp Problem Sp'13

  Volume of a Frustum  Sp'13