12/4/99

Amazing Number Fact No14

The factors of the central numbers in Pascal's Triangle follow a pattern:
1 = 1 x 1
2 = 2 x 1
6 = 3 x 2
20 = 4 x 5
70 = 5 x 14
etc
The sequence 1, 1, 2, 5, 14 ... are called the Catalan Numbers.
What have they got to do with the Bubbles Investigation ?
Why don't you try the investigation to find out?!!
If you want to know why Catalan Numbers are important try:
LINK1 or LINK2 or LINK3 or LINK4
Worksheet of the Week
The Share-out

19/3/99 - 12/4/99

We are closed for the Easter Break but...
there will be exciting new resources for you when we return.
Happy Easter!
 
When you devour that chocolate Easter Egg do you ever give a thought to...
The Mathematics of the EGG ?
There are worksheets available for this link.
The Featured Easter Holiday Mathematics Site
We highly recommend Coolmath ... a Site that has been designed for the pure enjoyment of mathematics by a mathematics enthusiast ... HAVE FUN!

19/3/99

Amazing Number Fact No13

What is amazing about the number 21322314?
And what has it to do with the sequence:
1
11
21
1112
3112
211213
?
If you are completely confused then FIND OUT

Worksheet of the Week

We are blowing BUBBLES this week.
Bubbles inside Bubbles inside Bubbles ...
but unfortuneately cannot supply you with the mixture

12/3/99

One of the SQA Higher investigations this year is "It's a Perfect Day". There are some interesting Sites on the Internet which give useful background to this investigation. We are compiling a list here.
You may like to visit Chaos Theory and Fractal Geometry .This Site has activities, demonstrations, and links to other Web sites. Topics covered include: The mathematics and history of Chaos Theory; Iterations and recursions; Dynamical systems and how they relate to real world situations; Graphing non-linear equations and the creation of strange attractors; The mathematics of fractals, including fractal generators for students to create their own fractals; Mandelbrot and Julia sets; Measurement and Scale.

A New Link

We highly recommend Interactive Mathematics Miscellany and Puzzles.
This Site contains a wealth of fascinating mathematics. Alexander Bogomolny, the constructor of the Site, has an infectious love of Mathematics. His Site is a work of art dedicated to spreading the word that Mathematics has great beauty, can be exciting and most of all is an intellectually stimulating adventure of discovery. Spend some time browsing... you will not be disappointed!

Amazing Number Fact No12

The HARMONIC NUMBERS are:
H1 = 1
H2 = 1 + 1/2 = 1.5
H3 = 1 + 1/2 + 1/3 = 1.8333 ...
H4 = 1 + 1/2 + 1/3 + 1/4 = 2.08333 ...
So just how large is Hn?
You might like to check on a calculator that H60 = 4.6798 ...
The 60th Prime Number is 281 and one 60th of 281 is 4.6833 ...
Is it just a coincidence that these answers are very close?
Calculate H100 (15 minutes at most!) and then find one 100th of the 100th prime and be amazed!
Read our previous Amazing Number Facts

5/3/99

Amazing Number Fact No11
 
Here is a remarkable formula: f(n) = n2-n+41
f(1) = 12-1+41 = 41 a prime number
f(2) = 22-2+41 = 43 a prime number
f(3) = 32-3+41 = 47 a prime number
f(4) = 42-4+41 = 53 a prime number
 
How many prime numbers does this formula produce?
A formula that always produces prime numbers in this way has never been found. So just how good is this formula at producing primes? You may need a list of prime numbers to help when you do your calculations. Good luck!
4/3/99
Counting in Greenlandic

So is there a Loopy Number in among this lot?

 
atuseq
mardluk
pingasut
sisamat
tatdlimat
arfineq (second hand)
arfineq-mardluk (second hand two)
arfineq-pingasut (second hand three)
arfineq-sisamat (second hand four)
arfineq-tatdlimat (second hand five) or qulit
arkaneq (first foot)
arkaneq-mardluk (first foot two)
arkaneq-pingasut (first foot three)
arkaneq-sisamat (first foot four
arkaneq-tatdlimat (first foot five)
arfersaneq (second foot)
arfersaneq-mardluk (second foot two)
arfersaneq-pingasut (second foot three)
arfersaneq-sisamat (second foot four)
arfersaneq-tatdlimat (second foot five) or inuk navdlugo (man counted out)
2/3/99
The Nrich Site
Some of our students have managed to solve The January Problems from the On-Line Interact Magazine. They are Alan Riddell and Peter Brittian from S6 and Claire Kruithof and Rhona Bagnall fom S2
 
You can read details in our February Diary.
26/2/99
Amazing Number Fact No10
 
3 x 37 = 111 and 1+1+1 = 3
6 x 37 = 222 and 2+2+2 = 6
9 x 37 = 333 and 3+3+3 = 9
...
continue this pattern and be amazed!
19/2/99
Are we not drawn onward, we few, drawn onward to new era?
Is this the palindromic rallying cry for the new millenium?

Amazing Number Fact No9

 
Let's multiply the first four positive integers together: 1x2x3x4 = 24. Obviously 5 does not divide 24 but it does divide 1 more than 24.
Now let's try the first five positive integers multiplied together: 1x2x3x4x5 = 120. This time 6 does divide 120 and does not divide 1 more than 120.
The next case is: 1x2x3x4x5x6 = 720. Does 7 divide this? Does 7 divide 1 more than 720?

n

1x2x...x(n-1)
divides by
n?

1x2x...x(n-1) + 1
divides by
n?

2

1

no

1+ 1

yes

3

1x2

no

1x2 + 1

yes

4

1x2x3

no

1x2x3 + 1

no

5

1x2x3x4

no

1x2x3x4 + 1

yes

6

1x2x3x4x5

yes

1x2x3x4x5 + 1

no

7

1x2x3x4x5x6

no

1x2x3x4x5x6 + 1

yes
Continue this table and observe something amazing about the pattern of yes/no answers in the last column.
What has this to do with a man called Wilson?

Read our previous Amazing Number Facts

15/2/99
Visit TOOTHPICK WORLD
Try our Valentine Puzzle
This is now the largest collection of toothpick puzzles on the Internet
Why not send your favourite Toothpick Puzzle to madrascollege.maths@fife.gov.uk and if we like it we'll publish it!
Amazing Number Fact No8

What property do the numbers 3 and 1501 share?

3 has factors 1 and 3 giving a total of 4 = 22 a square number: .
1501 = 19 x 79 a product of two primes and therefore has factors 1, 19, 79 and 1501.
The total of these factors is 1600 = 402 a square number.
Check that 22 also has this property.
Can you find the other three numbers less than 100 that have this property?

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