Tag: series

Fibonacci’s Sequence

Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa, is connected in most of our minds with the Fibonacci sequence. Spreadsheets make wonderful tools for creating such sequences. This one is amazingly simple. Just select a cell, any cell and write a formula in that cell that adds together the two cells above it. Now copy that cell down the spreadsheet and seed it with 1 in the first cell. The Fibonacci sequence is a pattern that this action shows very well. This sequence has surprising attributes, and we explore some of them as well.

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).

Lights Out

This is one of those math puzzles that come up in contests but which turn out to be quite interesting mathematically. Imagine a long hallway with lights in the ceiling, all on and each controlled by its own chain. A long line of people (as many as there are lights) walk down the hallway. The first one pulls every chain, the second one every other chain, the 3rd pulls every 3rd chain and so on. When all the people have walked down the hallway, what lights, if any, will still be lit? What more can you learn from this puzzle about multiplication?