High School Notebooks

by George Beck

Drawing Letters with Splines
                                                                                          [splines.ma]

Sign your name by having Mathematica connect the dots.

Long Multiplication and Division
                                                                                          [long.ma]

This shows the long multiplication and division of positive integers.

a x + b
                                                                                           [axplusb.ma]

What does changing a and b do to the graph of y = a x + b?

Parabolas
                                                                                           [parabolas.ma]

What does changing a, b, and c do to the graph of y = a x^2 + b x + c?

Why Is Pi the Same in C = 2 Pi r and A = Pi r^2?
                                                                                           [pi1.ma]

We slice up a circle like a pie and rearrange the sectors to form a figure that is roughly a rectangle. As the sectors become thinner, the rectangle's left and right sides become more vertical and the top and bottom become flatter and more horizontal. We can imagine that in the limit we get an actual rectangle.

Nesting Regular Polygons and Circles
                                                                                           [scribe.ma]

This notebook is under construction but the functions work. Circumscribe and Inscribe are functions that let you draw nested sequences of circles and regular polygons.

Approximating Pi
                                                                                            [pi2.ma]

This notebook shows how to approximate pi by using the areas of polygons.

Solving Quadratics Step by Step
                                                                                           [stepquad.ma]

This notebook discusses the solutions of quadratic equations in a several different ways. The built-in functions Solve, NSolve, and Factor give three fast  ways to solve a quadratic equation. Their solutions are easy to check.  The defined function WalkSolve solves a quadratic step-by-step by completing the square. We derive the QuadraticFormula and compare it with the Russian version.

Solving Linear Equations Step by Step
Two Equations in Two Unknowns
                                                                                           [step2by2.ma]

This notebook discusses the solutions of systems of equations  The built-in functions Solve and NSolve are the usual way to solve such systems.  The defined function WalkSolve solves a system step by step.

Step-by-Step Differentiation
                                                                                           [stepdiff.ma]

The built-in Mathematica operator D gives derivatives immediately without any intermediate steps. In this notebook the operators WalkD and RunD are defined to slow things down so that a beginner can learn how to take derivatives.

Ladders
                                                                                           [ladders.ma]

Are ladders too simple for math questions? These brain teasers might drive you up the wall.

Geometry of Complex Arithmetic
                                                                                            [i.ma]

The basic functions and arithmetic operations on complex numbers are discussed from the point of view of geometry.

Vieta's Formula
                                                                                            [pi3.ma]

This notebook continues the discussion on aproximating pi by calculating the areas of a circle using inscribed and circumscribed regular polygons. We illustrate Vieta's formula, which is the oldest exact result derived for pi.