The length of the day is something we take for granted. Yet, much can be learned about the day -- and the way the Earth moves -- from careful observations of the Sun and a more distant star, over as little as 24 hours, with a home-made viewer and a good clock.

There is a popular bumper sticker slogan which advises us to 'Think Globally, Act Locally'. But what does it really mean to 'think globally'? One meaning could be to try to estimate the global consequences of the things you do. Here is one way to go about this.

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.

Problem: Fire towers are built so firefighters in forested regions can scan large areas for potential trouble. Upper-story and penthouse apartments rent for the highest prices because of the terrific views. Assuming the atmosphere is clear, and there are no hills or mountains obstructing the view, how far could you see to the horizon from the top of a 100 meter fire tower? From the top of a 55 story skyscraper, where each floor is 3 meters high? From the top of the tallest building in the world (the Petronis Tower in Kuala Lumpur, Malaysia, 1,467 ft. high)?

This simple example shows how algebra can be useful in the real world: Should Grandpa start receiving his Social Security Benefits at age 62 or should he wait until age 65?

Mathematicians often argue that anything which can be represented numerically or algebraically can also be represented geometrically. This is perhaps true even to the
extent that simple numeric calculations can be demonstrated geometrically. The following example illustrates one such geometric process of addition.