Most museums with math exhibits have a Pascal’s triangle made up of pegs with balls falling down between them and bouncing off of them. One of the things they want to show is probability and the Normal or Bell curve produced by these balls as they fall down most of us are familiar with. This is the curve produced if we flip a honest coin a large number of times and ask what are the chances of getting all heads, of all heads but one and one tail, of getting all but 2 heads etc. We ask what does a Normal distribution look like and why does this extremely simple pattern produce it?
Category: Labs
Pascal’s Triangle
Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that adds the two cells in a row (horizontal) above it. This pattern is like Fibonacci’s in that both are the addition of two cells, but Pascal’s is spatially different and produces extraordinary results. Pascal’’ triangle is related to an amazing variety of mathematics, things like Fibonacci’s sequences, the triangular numbers, the powers of 2, the binomial theorem, the Bell curve, and more, so much more. We invite you to explore!
Parentheses and Pi
Parentheses are very important in spreadsheets because like all programming, spreadsheet formulas have to be very specific. A big formula, especially one like Viete’s approximation of pi, likely will require us to think both in parentheses and in creating formulas that naturally build a series. This one is quite interesting and you will know if you are approaching the right answer if you are approaching the value of pi. So be careful and watch your (parentheses).
Pennies to Heaven
Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of the greatest experimental and theoretical physicists of the 20th century, are real-world estimation problems. So we ask, “If we had a stack of pennies as tall as the Empire State Building, how big a room would we need to hold them?” Like most Fermi problems the answer to this one is a delightful surprise and requires us to think out-of-the-box. Always ask, “What do you guess?” “Would you need a whole house or something bigger, just your bedroom, or a closet, or something even smaller?”
Decimals and Percents
Ratios can be written in a wide variety of different way: as fractions, as decimals, and as percents.,with a colon, with a slash, as a fraction and even as a baseball batting average. Here we compare a decimal ratio and a percent by building decimal and percent tables in the same way and compare their patterns to the ratio patterns we are used to. Ask students what other ways of expressing ratios are there.