Math game 1 updated

Here is the updated version of math game 1. Hooray!

Math game one

Enjoy

Rubik's Cube

Do you know what a rubik's cube is? Well, it is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

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The Mathematics in it:

The original (3×3×3) Rubik's Cube has eight corners and twelve

edges. There are 8! (40,320) ways to arrange the corner cubes.

Seven can be oriented independently, and the orientation of the eighth depends on the

preceding seven, giving 37 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange

the edges, since an odd permutation of the corners implies an odd permutation of the edges as

well. Eleven edges can be flipped independently, with the flip of the twelfth depending on the

preceding ones, giving 211 (2,048) possibilities.

There are exactly 43,252,003,274,489,856,000 possibilities, which is approximately forty-three

quintillion!!! Can you believe that??

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-Algorithms

In Rubik's cubists' parlance, a memorised sequence of moves that has a desired effect on the cube is called an algorithm. This terminology is derived from the mathematical use of algorithm, meaning a list of well-defined instructions for performing a task from a given initial state, through well-defined successive states, to a desired end-state. Each method of solving the Rubik's cube employs its own set of algorithms, together with descriptions of what the effect of the algorithm is, and when it can be used to bring the cube closer to being solved.

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P.S. "!" means factorial.

1 Factorial= 1

2 Factorial= 1x2

3 Factorial= 1x2x3

4 Factorial= 1x2x3x4

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More information on factorial

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Anyway to those who know how to solve the Rubik's Cube, please post your fastest timing here. Thanks!

Regards,

This Math Team

Pi - Infinity and beyond... Lesson 5

Secondary One Mathematcis

Have you learnt what π is?? Well if you don't,

you would have probably failed your PSLE Mathematics. The number π,
defined as the ratio of

the circumference of a circle to its diameter, has been an object of curiosity and study to

mathematicians for thousands of years. Although it rises from one of the simplest and most

symmetric shapes, it presents many mathematical mysteries: it is irrational, and indeed,

transcendental. It is one of the so-called fundamental constants – it appears in important roles

in geometry, trigonometry, and even in unexpected fields like statistics. People memorise its

digits to the thousandth

decimal place and search for patterns in its decimal expansion; they develop computer

algorithms to find its billionth digit and beyond.

Nobody knows who the person was that first defined π, or that first estimated it. As long as

people have built permanent structures or measured things, there has likely been some

awareness of the number. There is evidence that approximations to π were used by the ancient

Mesopotamians at the beginning of recorded history. In early written fragments from the

ancient Egyptians and Babylonians, we find accounts of measuring circles.

The early approximations were doubtlessly discovered simply by measurement – rough

estimates for π can be made using as little as a rope and a large circular object. Although not

very accurate, the ancient Babylonian value of 25/8 and Egyptian value of 256/81 were good

enough for most architectural purposes.To date, Mathemticians have discovered millions and

millions of digits of pi, and it keeps going on and on and on... In simple words, π is an irrational

number, which means thst the number keeps on going on forever till the cows come home.


Picture: http://upload.wikimedia.org/wikipedia/commons/4/4a/Pi-unrolled_slow.gif


Other examples of irrational numbers: e , π, √2


Examples of rational numbers: √121, 4/4 etc.


Here is the link to the printable version of the million digits of pi(which contains more than 320 pages) Enjoy!!



More information

The million digits of pi


Regards,

This Math team.



Acknowledgement: http://en.wikipedia.org/wiki/File:Pi-unrolled-720.gif


Here is a video:

Mathematics Concept Map

This is the link to lesson 4(even though the file is called lesson 3) and here is a concept map on Mathematics. Enjoy. Click on the picture to enlarge image.

Link: http://the-chronicles-of-pi.ning.com/profiles/blogs/lesson-3

P.S. The daily contest is now open to contestants!! Fantastic prizes to be won!!!