# Browse

## You are looking at 11 - 15 of 15items for :

• Functions and Trigonometry
• Computers
• Refine by Access: All content
Clear All
Restricted access

## The Shape of an Ellipse

Ellipses vary in shape from circular to nearly parabolic. An ellipse's eccentricity indicates the location of its foci, but its aspect ratio is a direct measure of its shape.

Restricted access

## Activities for Students: The Hands Project

The author presents an activity in which the lines in students' hands are analyzed, with curves and lines fit to each one.

Restricted access

## Delving Deeper: Deepening Understanding of Transformation through Proof

In the introductory geometry courses that we teach, students spend significant time proving geometric results. Students who conclude that angles are congruent because “they look that way” are reminded that visual information fails to provide conclusive mathematical evidence. Likewise, numerous examples suggesting a particular result should be viewed with skepticism. After all, unfore–seen counterexamples render seemingly valid conclusions false. Inductive reasoning, although useful for generating conjectures, does not replace proof as a means of verification.

Restricted access

## Flower Power – Sunflowers as a Model for Logistic Growth

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy (see fig. 1). The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population, capacity is defined as “the maximum population that the environment is capable of sustaining in the long run” (Stewart 2008, p. 628).

Restricted access

## An Excel–lent Card Trick

Card tricks based on mathematical principles can be a great way to get students interested in exploring some important mathematical ideas. Bonomo (2008) describes several variations of a card trick that rely on nested floor functions, but these generally go beyond the reach of beginning algebra students. However, a simple spreadsheet implementation shows students why the card trick works and allows them to explore several variations. As an added bonus, students are introduced to composite functions, the floor function, and iteration, and they learn how to use formulas and the INT function in Microsoft Excel. The depth of the mathematical explanation can be varied according to students' background.