# Science and Math

by David P. Stern
http://www.phy6.org/stargaze/Sstern.htm

 Science Standards in Physics, Astronomy and Earth Sciences       A proposed list of science standards for public schools, submitted to the state of Maryland in 1998. Continued Fractions       Decimal fractions can represent any number to different degrees of precision, depending on where we cut off their expansion. Continued fractions are a little-known way of doing the same using ordinary fractions. This is a very elementary exposition, suitable for public school math enrichment. A Different Kind of Multiplication       Addition with Roman numerals is relatively straightforward (especially if you use an abacus), but they are poorly adapted for multiplication. Yet the Romans did have a method, described here. It is based on the binary system of representing numbers, though of course they did not realize that. Solving a Sudoku puzzle       A Sudoku puzzle centers on a square array of 81 cells, with 9 rows of 9 cells each. In the array, each line is expected to contain the numbers (1, 2, 3 ... 9) in a different order, and so does each column: in neither case is any number repeated. In addition, however, the array can be divided into 9 smaller 3-by-3 squares, each of which is also to contain (1,2,3....9) with no repetition. In fact many such arrays exist.         The challenge of the puzzle is--given a square array of 81 cells in which just some of the cells contain their numbers, use logic to deduce all of the others. This web page uses a specific example to present some of the methods one can use. Solving a Harder Sudoku puzzle       If you have finished the preceding web page, and look for a tougher challenge--here it is! Again, a step-by-step solution is given, providing some ideas about dealing with puzzles of the "evil" or "diabolical" kind. A Frying-Pan Electrophorus       an experiment using mostly kitchen equipment, suggesting that static electricity (such as can flash a neon bulb) and chemical electricity from a flashlight cell do in fact have the same nature. Suitable for classroom demo or science fair project.     Spanish Translation by Horacio Chávez. The Grease-Spot Photometer       a simple experiment or demonstration, confirming the claim that the intensity of illumination decreases like 1/R2, where R is the distance from the source of light. Most of what you need is paper, cardboard, candles or flashlight bulbs wired to a source of electricity--and just a little dab of oil. Secrets of the Polar Aurora       The bright displays of polar aurora are caused by fast electrons arriving from space and striking atmospheric atoms about 100 km (60 miles) overhead. This illustrated article, adapted from a talk given in Alaska, discusses the origin of the aurora, its magnetic control, its connection to the Sun's activity, artificial auroras and auroras at the planet Jupiter.     Spanish Translation by Thamara Quintini (part of the collection "Exploration of the Earth's Magnetosphere"). All I Really Need to Know about Physics I had to Dig Up by Myself.       Lessons of the career of a physics researcher. ;