# M1.4.7

**arguments as justification**for solutions to specific problems and for algorithms constructed for various purposes.

### Proving the Pythagorean Theorem

A guided classroom exercise that contributes to the long-term development of creative thinking and analysis.

### Battle Strategies in the Bismarck Sea

Opposing naval commanders in a war must choose how to attack and defend rncritical areas.

### Motivating Honest Budgets and Hard Work Simultaneously

Motivating honest budgets and profit expectations is difficult because some rnsubordinate managers will provide overly optimistic budgets to "look good" to rntheir bosses, while others will lowball budgets so they will "look good" when they rnexceed expectations. This paper explains how to motivate accurate forecasts of rnbudgets and profits.

### Finding All Solutions to a Puzzle

The non-zero digits can be organized into a 3-by-3 array such that each row, rneach column, and each diagonal adds up to the same total. How many solutions rnare there? Find and describe them.

### Thermo and Fluid Dynamics of a Homemade Lava Lamp

Lava lamps are just cool, that's all there is to it. Most everyone has spent at least an hour of their life just staring at a lava lamp. While the experiment outlined here isn't really the same as a commercial lava lamp it does demonstrate many of the important fluid and thermodynamic properties. Most importantly it provides students with an interesting and fun visual demonstration intended to motivate thought about the physics behind the experiment itself.

### Learning from Slide Rules

In the days before calculators and personal computers an engineer always had a slide rule nearby. These days it is difficult to locate a slide rule outside of a museum.

I don't know how many of those who have used a slide rule ever thought of it as an analog computer, but that is really what it is. As such, the slide rule can be used to teach the modern view of the relationship between nature and mathematics and about the formalization of this concept known as isomorphism, which is one of the most pervasive and important concepts in mathematics.