The New Turkish Currency

In 2009, the New Turlish Lira (YTL) will be renamed simply the Turkish Lira (TL). What does this have to do with math. Well... to my great surprise, they have a mathematician on the 10TL note. Here is the information from the Turkish Mint: "The back of the note features a portrait of Ord. Prof. Dr. Cahit Arf (1910 – 1997). Cahit Arf was one of the most significant mathematicians of Turkey and is renowned internationally for many theorems in his name. Other elements on the back of the banknote are mathematical motifs consisting of a section of Cahit Arf’s “Arf Invariant” as well as “arithmetical progressions, an abacus, numbers and figures that represent the binary system, which is the basis of computer technology. "

Continuous Probability Function

Here is an example of a CDF problem. Try to solve it manually and check your answer using the CDF Geogebra applet. Email me if you want to change the function. I will send you the .ggb file that you can alter and play with.

This Week's Number: 7

We were talking in class about probability. Here is a podcast on the number 7. What does this number have to do with probability? Well is a central number to the study of riffle shuffling. Listen to BBC radio’s series on numbers. The episode is titled "The Number Seven". It is a radio series hosted by Simon Singh.

The Normal Distribuiton

Here are two applets that I created to help you visualize the normal distribution. The first applet shows how the graph changes given a different mean and/or standard deviation. The shape is of course always a 'bell curve'. The second applet is better suited if you want to look at probabilities with data that is normally distributed. Notice how the function that generates this curve contains both pi as well as the natural base, e. The importance of these numbers cannot be underestimated.

Cellphone Tower Problem

What cellphone towers are responsible for a given area in a city? This is the problem was given in class along with the rubric and the Geogebra solution.

Voronoi Diagrams

To review some basics in Algebra in SL Math, we played with Voronoi Diagrams. Here is the problem that was asked and the solution using Geogebra. There are many fascinating sites about these diagrams. Explore these sites: Voronoi Game 1, Voronoi Game 2 (and an introduction to the idea behind the game), A paper on Ornamental Design using these diagrams with a web gallery, a very brief explanation on how to generate fractals using these diagrams, an art installation that I would love to build about the idea of personal space, another fractal site, finally some images and explanations (also on wikipedia). I apparently went a little crazy looking up some of these things.

Three Planes Question

Here is a little question about the intersection of three planes. There is also a movie to help you visualize. The planes move through the values of k through 0 to -5. (That should give you a rough idea of the possible range for the answer)

Gödel’s Incompleteness Theorems

There should be more place for the philosophy and history of mathematics presented to students. There are some decent resources on the web and there has been more research done on the history of mathematics recently. There are many misconceptions in mathematics and its foundations. Here is a BBC radio program about the foundations of mathematics. You may be surprised by what is discussed. The program is called "GÖDEL'S INCOMPLETENESS THEOREMS" and subtitled "The Dirty Secrets of Maths". If people only knew...

A Math Podcast

There is a pretty good podcast out there about math. Even your ipod is not safe from becoming an educational tool. The Math Factor has short audio discussions about math but to make it worth it, you should look at the website to see the write up about the topic. There are quite a few interesting ideas in there. Browse around.

Oct.21-24

Here is this weeks lessons and homework. Enjoy. Oct.21-24
Don't forget to go to the main website for worksheets, extra practice, extra links, quizzes, etc...

Easy Math Puzzles

Here are little math puzzles courtesy of BBC Radio.

Question of the Week

Here is a challenge for all students. Try to prove this little geometric construction. We will discuss it in Math Society at lunch on Wednesday. Come with your attempt(s) at the solution.

Photography and Your Graphing Calculator

Here is another use for your favorite graphing Calculator. Turn it into an Intervalometer for your time lapse photography. Go to Instructables for explanations.

Geometry of Trig Ratios

Here is a little challenge for you. Prove that all the trig ratios can be drawn on the unit circle. Enjoy! Select "The unit circle on Geogebra" to see the unit circle with the ratios. If you want the unit circle and ratios without the challenge questions select "Unit Circle 1" and if you want the unit circle, ratios and their associated graphs select "Unit Circle 2"

Oct.13-17

Here is this weeks lessons and homework. Enjoy. Oct.13-17
Don't forget to go to the main website for worksheets, extra practice, extra links, quizzes, etc...

Video: Dimensions

There is a wonderful series of short videos called "Dimensions" created by Jos Leys, Étienne Ghys and Aurélien Alvarez. It is a strikingly beautiful series that is free for download or watching online. Since we finished complex numbers in HL Math in grade 12, I thought I would post the link to 2 chapters on the subject: chapters 5 and 6. The end segment on complex numbers contains some mezmerising graphics. Details on these chapters are also online if you would like to read more about the information in the videos. From the website: "One should consider these chapters as supplementary, as illustrations which encourage further learning or maybe as reminders of lessons forgotten long ago. Certainly the film tries above all to show clearly the geometric side of complex numbers."
Below is an image from the final sequence of chapter 6.

Canadian Mathematics Competition

The University of Waterloo has organized the Canadian Mathematics Competition contests. These are contests designed for every grade from 7 to 12. They also post the past contests on their website. This means that you have access to the past nine years of math contests from them. It is a great source to practice your math skills. Some of the last questions in part C of the contests can be worthy of further exploration. Here is an example of what can be done using the free Geogebra math software.

This Week's Number: i

In the IB HL grade 12 class, we completed our exploration of complex numbers. Listen to BBC radio’s series on numbers. The episode is titled "The Imaginary Number". It is a radio series hosted by Simon Singh. Here is also the two short proofs we discussed in class for Euler's exponential form of complex numbers.

Book Review

"1089 AND ALL THAT" by David Acheson is a tiny book which provides an excellent overview of mathematics. Using an informal approach and plenty of humor, Mr. Acheson presents profound ideas with neat puzzles, illustrations and cartoons along with his concise writing. You can find it in the BUPS library. Of course, you can always order a copy of your own from your local bookstore or internet retailer! Highly recommended.

Contest Question

Here is a question from the 2007 Cayley Contest from the Canadian Mathematics Competition.
Square in a Square Problem

Dividing a Square

Here is a simple problem: Cut a unit square into 5 triangles whose areas are in geometric progression. Seems easy but the mathematical solution is not always as easy as it first seems. Here is the solution we came up with. Do you have other suggesstions?

Oct.6-10

Here is this weeks lessons and homework. Enjoy. Oct.6-10
Don't forget to go to the main website for worksheets, extra practice, extra links, quizzes, etc...

Sept 22-26

Here is this weeks lessons and homework. Enjoy. Sept22-26
Don't forget to go to the main website for worksheets, extra practice, extra links, quizzes, etc...

12.9 Million Digits

The Largest Prime Number Is Now 12.9 Million Digits! These come up once in a while but the fact that it is greater than 10 million digits makes it the winner of a $100000 prize. Here is a little news article on it. For more information on prime numbers try primes.utm.edu. The image shows the start of how you would pronounce the number.

Are you a math whiz?

Are you a math whiz? Care to test some recent research ideas? Here is an article from the New York Times that your 'number sense' to approximate quantities of objects can predict your success in math class. "One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses." What do you think? Try the test at home. This is definitely going to be something to play with in class next week.Read the article and take the test: "Gut Instinct's Surprising Role In Math".

The Golden Ratio

Since we are going over sequences and series in IB1, we can visit a ratio related to the Fibonacci sequence (you know... 1,1,2,3,5,8,13,21,etc..). Listen to BBC radio’s series on numbers. The episode is titled "The Golden Ratio". It is a radio series hosted by Simon Singh.

Sept 15-19

Here is this week's lesson plan. Remember... this is where all your homework is posted in case you lose your agenda.
Sept15-19

Triangle Problem

Here is a little exploration problem I created with GeoGebra. Enjoy! File: Triangleratio

Sept. 8-12

This week's offering in our math classes...
http://web.mac.com/thesliderule/iWeb/LacosteSite/Lessons.html

This Week's Number: 1

Boring plain old 1? Maybe not... It's the number used to catch people lying on their tax returns or other numerical data. Listen to BBC radio’s series on numbers. The episode is titled “1 - The Most Popular Number!”. It is a series hosted by Simon Singh.

Waiting For The Bus

Here is a major breakthrough in mathematical research... The paper is titled “Walk versus Wait: The Lazy Mathematician Wins”. A must read.