Middle School (6-8)

Square Root of 2: Irrational, Yes! Impractical, No!

For the mathematically inclined person, irrational numbers such as a² are fascinating, both from a historical perspective, and as a classic example of using the reductio ad absurdum proof, to prove the irrationality of a². However, the majority of students, when introduced to the irrational number a², might be excused for not being fascinated by it, and might believe that a² has not much practical use.

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Seeing Interference Fringes

Demonstrate the wave nature of light by projecting interference patterns. Detecting the interference of waves is one of the most powerful methods in science for measuring wave phenomena, and using the waves and their interference can reveal underlying details of their sources and the materials through which they travel.

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Rotational Motion and Rocket Launches

My friend Kyle works for Boeing on the Sea-Launch project. Sea-Launch is a portable, floating rocket launch pad for putting satellites into space. So, if Korea wants Sea-Launch to put a new digital TV satellite into space, and Sea-Launch can go anywhere in the world with water, where should Kyle take Sea-Launch? (No, it doesn't have a steering wheel. It gets pulled by tugboats.) Well, like any scientist, he scratches his head for a minute, then works it out. Grab a pencil and follow along!

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Particle Man and the Photon

When a photon ( a very small increment of energy) encounters a substance one of three things may happen. (1) The photon may be transmitted -- it passes through without alteration. (2) The photon may be absorbed -- the photon never leaves the particle. (3) The photon may be scattered -- it's path may be altered.

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Mixing and Stirring

Combining two fluids (confluence of two rivers, Mediterranean water spilling over the straits of Gibraltar into the Atlantic) involves two processes: (1) stirring -- stretching of the bulk fluid, and (2) mixing -- exchange of materials on the molecular level (diffusion).

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Making Months

It is easy to take our calendar, with its system of weeks and months, for granted. But this system is really just a societal choice -- it has been debated and modified in the past. It will also have to be re-examined when humans colonize other planets. 'Making Months' illustrates a use of factoring, in a decision-making process.

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Just What is a Logarithm, Anyway?

Before we talk about logarithms, let's think a little bit about graphing.

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Ice Sheets and Sea Level Rise

The ice sheets of Greenland and Antarctica contain massive amounts of frozen water (i.e., ice) that, if broken off or melted, for instance from extended global warming or from outward ice flow, would go largely into the oceans. In view of the vast size of the oceans, covering over 70% of the Earth's surface area, many people might at first think that the addition of ice or melted ice from the ice sheets would have little impact on global sea level.

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How Thick is the Atmosphere?

We've all seen pictures of the Earth and its atmosphere as a series of concentric circles, showing the troposphere, stratosphere, ionosphere, etc., often looking like a bullseye target with the solid Earth in the middle. But if we were to draw that picture to scale, what would it really look like?

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How Now, Pythagoras?

You may think of the Pythagorean theorem as useful only to geeky college freshmen who want to calculate how many steps they are saving by walking across the grass. Recently I learned of a very practical use of this theorem in a very unexpected place.

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