I've been a math enthusiast for ages. My academic work includes a late-in-life M.S. in Mathematics, and my professional work included math teaching and tutoring. Since I've also worked and hobbied as a computer programmer, I've combined the interests in a number of math-related programming experiments. Check out some of the results!
- Arithmetic
- A matching game to practice arithmetic with both whole numbers and fractions. (MathML)
- Geometry
- Pythagorean Theorem - Demonstrates the Pythagorean Theorem by repositioning four a-by-b right triangles within a (a+b)-sided square. (Geogebra)
- Pythagorean Triples - Explore sets of integers that can form the sides of a right triangle.
- Triangle congruences - Is the information given enough to guarantee
triangle congruency? (Geogebra)
- Angle and Opposite Side
- Angle - Side - Angle (Two angles and the side length between them)
- Side - Side - Side (Three sides)
- Angle - Side - Side (Two sides and a non-included angle.)
- Side - Angle - Side (Two sides and the included angle.)
- Triangle congruence applications - Why does it matter? (Geogebra)
- Where's the Fire? - Triangulation by Angle-Side-Angle
- Steady my bookcase! - Structural integrity of Side-Side-Side
- Sometimes SSA - restricted conditions under which SSA is a valid congruence.
- Triangle centers
- ConsIncenter - Constructing the incenter
- ConsCircumcenter - Constructing the circumcenter
- Incenter - Intersection of angle bisectors
- Circumcenter - Intersection of perpendicular bisectors
- Centroid - Intersection of medians
- Circles
- Circle Angles - How do central angles compare with other angles that intercept the same arc?
- Inscribed Angles - What's special about the relationship between central angles and inscribed angles?
- Inscribed Angle Chase - Find the measure of an inscribed angle using the Isosceles Triangle Theorem.
- Lighthouse - Use the measure of the inscribed angle to determine whether the boat is inside or outside of the danger zone.
- Diameter Inscribed Angle - Move from observation to proof that an angle inscribed on a diameter is a right angle.
- Inscribed Angle Proof - Explore the reasoning behind the Inscribed Angle Theorem. (Note - this only shows one of two or three cases, but their proofs are similar.)
- Inscribed Quadrilateral - What is the relationship between opposite angles of an inscribed quadrilateral?
- Inscribed Rectangle? - How could you tell if an inscribed quadrilateral is a rectangle?
- Trigonometry
- A matching game to practice recognizing trig values of common angles. (MathML)
- Calculus
-
The Derivative
Input (and optionally hide) a function, then explore. Options include color-coding the function for increasing/decreasing or for concavity. The tangent line at a point can be viewed, as well as graphs of the first and second derivatives. (Geogebra)
- Continuity
Explore the epsilon-delta definition of continuity. Move a point on the graph, set your epsilon, and find a sufficiently small delta. (Geogebra)
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The Derivative
Other stuff:
- Geogebra Examples
I like playing with this versatile and free tool. Most of my older examples need to be converted and posted, but I'll get there slowly.
- The Bellman Forest Problem
This was the topic of my master's research paper. Basically, the problem supposes you're lost in a forest of known dimensions but no way of telling where you are or which direction you are facing. Your job is to find the shortest path guaranteed to get you out of the forest.
- Brent's Real Riddles
I met Brent at Kent State when we were both doing graduate work. (He finished.) His collection of Real Riddles, often with a mathematical bent, is a fascinating bunch of puzzlers. One of them is the basis for the OddBall investigation below.
- OddBall / Teacher notes and program
The challenge: There are twelve balls, one of which may be heavier or lighter than the rest (or there may be no "odd ball"). You have three weighings with a balance scale to detect the odd ball (if present) and say whether it is lighter or heavier.
This is an attempt to explore mathematical thinking by tackling a hard problem. Includes a demo program (for Windows).
- Programming Experiments
A mixed bag of programming, mostly attempts to get math to work on the web. Or to give me some programming practice. Or both. Or whatever.
Includes:
- Matrix row operations and solving simultaneous equations (php with MathJax)
- Illustrating the Simplex Method (javascript)
- Math Matching Games (sadly Firefox only, using MathML)