Who was this man, Fibonacci?  And what more can we find out about his work and his sequence? Click on the file name below to see some remarkable patterns.
Fibonacci, the Mathematician

One of the sequences we have seen over the last two days is the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21,…  It has some really neat uses, patterns, and ratios. The Golden Ratio is part of this sequence, and it too, has great applications. Over the next three days we will explore [...]

Today, we look at the answers to yesterday’s questions. If you did not see yesterday, try them first before looking at the answers!  We also show how each is worked out and give it a name if possible. These will be analyzed in more depth over the next two days and next week. Click on [...]

One of the really neat things in Math is observing and analyzing sequences and their ratios. We start with an introduction, on Monday, and carry the theme throughout the week.  Click on the comic to enlarge, if needed.
 

I really like this puzzle in that when you first see it, you think that there is not enough information given to solve it. In fact, you even think that some of the information is weird, and useless. However, as soon as you start to apply some simple logic, out pops the answer!  Click on [...]

It is true, not only can I look into the future, I can also read your mind!! Here is a neat little math trick, with how it works as well, that will get your audience believing that you are a mind reader. Please watch the video and then click on the pdf file to see [...]

This week we have seen the musical scale’s evolution from the simple ratio of 4 : 5 : 6 of the major triad up to the full frequencies of the 12 semi-tone musical scale. Today we look at how graphing sine waves, usually a grade 12 topic, can help us understand why notes may harmonize. [...]

Better known for his Pythagorean Theorem about right triangles, Pythagoras (or his followers, the Pythagoreans) also researched the musical scale and discovered some of the underlying mathematics of the scale. Please click on the name of the file below to read about his accomplishments.
Pythagoras, Music and Triangles

After two days, starting with a simple ratio of 4 : 5 : 6, we now finish off the build up of the modern keyboard. We have used in the last two days simple ratio multiplying and fraction multiplying. Today we use our knowledge of geometric sequences to finish the job. Please click on the [...]

Carrying on from yesterday, we now finish off the C major scale, using only ratios and fractions. Tomorrow, we will look at why the black keys appeared.