6. VSF 2007 Project Information
Grade Grouping: 10
Team Size: 5
Subject Area: Computer Science
Project Type: Descriptive
Project Format: Traditional
Software Tools:
Website:
iWeb (Apple Computer, Inc.)
Mathematica 5.2
Adobe Photoshop CS
Adobe GoLive CS
Project:
Mathematica 5.2
Special Skills:
Website:
HTML
Retouch by Photoshop
Project:
Knowledge of Mathematica programming language
Hardware Tools:
MacBook with Mac OSX 10.4.8
iMac with OSX 10.4
PC with Windows XP
Source of Idea:
We started on this project 1 year ago, but we used the results of some graduates of our school.
Our teacher and his former students discovered Pascal-like triangles 5 years ago. This triangle was made from a game of probability theory. See Reference [4] and [5].
We generalized the triangle by increasing the number of players.
Calculating the problem was quite difficult and we used the computer algebra system Mathematica.
After that we made Sierpinski-like Gaskets from the Pascal-like triangles. These Sierpinski-like Gaskets are very interesting from the viewpoint of mathematics and computer science, and our results are published in Reference [9].
Using Mathematica we made a lot of calculations, and we discovered Fibonacci-like sequences.
When we discovered Fibonacci-like sequences, we began to study the relation between these Fibonacci-like sequences and the well known Fibonacci sequence.
It took us more than 2 months to discover some beautiful relationships between these two types of sequences.
These relationships will be published in [8].
When we made this web pages, we used a lot of mathematical formulas, but it was very difficult to display them properly.
The positions of formulas vary depending on the OS of computers.
Awards Received:
Our results have been published in [9]. This is a journal for scientists and artists who are interested in mathematics. Our research activity was introduced in Reference [10], and some mathematicians who read [10] invited us to talk at the Research Institute of Mathematical Science of Kyoto National University. We are the first group of high school students to talk at this world famous institute of mathematics in its history.
We have been invited to talk at Suri-no-Tsubasa Seminar at Tokyo National University. This seminar was organized by Dr.H.Hironaka who is a Fields Medal winner. We presented our research to a panel of famous mathematicians and 50 high school students selected from all across Japan.
Copyright:
We have already published lemmas and theorems in Section 2 and 3 in Reference [9]. Professor Slavik Jablan, the editor of [9], gave us permission to use all of the results we presented in the journal.
All the computer graphics are made by the authors using Mathematica. The authors drew the pictures of Pascal, Fibonacci, Sierpinski and a hand.
The third graphic on the page of pictures was created by Masakazu Naito who is a new member of our research group. He is not a registered member of this project.
Thanks:
We would like to express thanks to our English teacher Mr. Harrison Gray for correcting our English. If there are still some mistakes in our English, it is our fault. We did not have enough time to show him our finished article before submitting it.
We also would like to thank M. Daisuke Minematsu for helping us in doing the research and making home pages.
