*Virginia Beach Presentation, January 11, 2000*

Michael Fowler, University of Virginia

The first question, of course, is why do it at all? Don't we just want to get the basic facts and methods of science across? Why clutter it up with historical detail that is no longer necessary for an understanding of the actual science?

Well, I'm not claiming that every part of science will benefit from an historical presentation, but I have found it to be very effective over a wide range. Let me give some examples.

Let's begin with earth science. Perhaps one of the most basic facts of earth science is the actual size of the earth. I begin by asking the class who first gave a pretty accurate figure for how far it is around the earth. Most of them are amazed that it was Eratosthenes in the second century B.C! They didn't think anyone even realized the earth was round before Columbus.

Then I tell how Eratosthenes noticed the sun was exactly overhead on midsummer's day in Syene, but 500 miles to the north at Alexandria, it wasn't—in fact it was seven degrees off vertical. At this point I bring out a globe, a lamp (the sun) and a little flat head nail. I find Syene (it's now called Aswan) and move the flat head nail around, flat head against the globe surface, watching the shadow of the spike, until they get the idea. Then I try to get them to draw the diagram to see how this might give the size of the earth. It's better if they're in little groups, each group having a globe, etc.

The fact that this was midsummer's day means the globe has to be oriented appropriately with the northern hemisphere getting maximum sunlight. This leads naturally to a discussion of the seasons, demonstrated by walking the globe around the sun, keeping the axis always pointing towards the same star (Polaris). (Of course, this also brings in the apparent motion of the stars in the night sky, and why Polaris never moves.)

The Greeks also knew all about the phases of the moon. I use a Styrofoam ball for my moon, and it's much more effective if you can use a small video camera to give the view from the earth. For example, you can show what a rising moon looks like from different hemispheres.

The Greeks actually figured out the distance to the moon fairly well—see my notes. I think working closely with the globe, trying to visualize the earth-moon-sun system, and then thinking about the planets, is very good for developing a geometric and three dimensional intuition that is difficult to get in any other way.

Also, it's good to challenge the students to level the playing field between them and the ancient Greeks—what can they figure out by just watching the sky and thinking about it?

I have three sets of exercises on the web from a summer course for teachers, Global Exercises, Quiz 1 and Quiz 2.

Galileo understood much better than most Hollywood producers that a giant man, ten times taller than an ordinary man, and in proportion, would break his leg on the first step. Galileo understood the simple mathematical concept of scaling.

The essential point with the giant is that his weight would be a thousand times that of a man, but the cross sectional area of his bones, the bone that has to support the weight, would only be a hundred times greater. So the stress on each bit of bone would be ten times that in man, and although there is a built in safety factor, it isn't as high as ten, so the giant bone will soon break.

I have discovered on teaching this to nonscientist college first year students that in fact they don't really understand areas and volumes except for rectangles. Well, they have memorized the formula for a circle, but they don't usually understand it.

I start with a simple linear puzzle: imagine the earth is a smooth sphere, and a rope goes around the equator, lying on the ground. Now a second rope is placed above the first, just one foot higher all the way around the earth. How long is the second rope?

Then on to areas: draw a square. Draw one with sides double the length. It's pretty easy to see that the area is four times bigger. In fact, you can prove it by placing four little squares in the big one. But what about two circles, radii 1 and 2? You can't fit four little circles in the big one. One way to make it plausible is to inscribe a little circle in a square, so that it's just touching all four sides, then do the same for the big circle. It's clear that they fill the same percentage of the square. Another approach is to draw them on graph paper, count squares. This method of course works for any shape. Or, you could approximate the circle by a hexagon, etc. Of course, the most satisfactory way of finding the area of a circle is to slice it like a pie into very thin wedges, then take out the wedges and reform them into a rectangle by lining them up with their points alternating in direction.

On to volumes: it's good to work with simple cubic building blocks. Build cubes of side 2 and side 3. Count to find the volume and also find the surface areas. Write them down. It's also effective to take a one inch steel ball bearing, and a bag of half inch ball bearings, and ask how many of the half inch balls will balance the one inch ball on scales. A depressing number of students, in my experience, guess 4.

Here's a question on scaling they'll like:

In an experiment on scaling carried out in 1883, a dog of mass 3 kg. and surface area 2500 sq. cm. was found to need 300 calories a day to stay alive and warm (no exercise or weight change). Another dog of mass 30 kg. and surface area 10,000 sq. cm. was found to need 1100 calories a day.

(a) Do the calorie requirements correlate better with mass or surface area? Explain what you would expect. How precise would you expect the correlation to be?

(b) Make an estimate of your own mass and surface area, and, assuming you are doglike for purposes of this question, how many calories do you need a day to stay alive, without exercise and at constant weight?

I have always found the concept of acceleration very difficult to teach, although maybe, at least for linear acceleration, the motion sensors are an effective tool. However, I've had some success in just reproducing Galileo's original ramp experiment, using students to run it, including the water clock to time it. This is fun, and explaining the results with them drawing graphs helps understand acceleration. Also, it's good to read Galileo's own description of the experiment, to see how close you are to the original.

Even more enlightening is to go on from that to just drop a ball and video it, then play it back frame by frame, marking where the ball is, to find *g*. This is *much* more effective than using a canned presentation. This is real—the students see themselves dropping the ball on the video.

I have a selection of applets I've used to teach physics, these are all written by me or my graduate student, so feel free to use them in your teaching (but not commercially). My own favorite is Newton's Mountain. Newton would have put this applet in the CD version of *Principia*, if he'd been able to! Newton's great breakthrough was to connect the motion of the moon and planets with ordinary everyday motion of things on earth. This applet takes Newton's own diagram and animates it.

Just Google Galileo Einstein to find my website. In general, type in the person or topic, then add fowler, and Google will have my lecture not too far down its list.

I've given a course on Modern Physics for second year physics majors. However, some of the lectures contain material that has been used in high schools here and in England. Here's a list of reasonably accessible lectures:

Evolution of the Atomic Concept and the Beginnings of Modern Chemistry

From Bohr's Atom to Electron Waves