Magnificent+Maths+WestGATE+2012

**• some interesting numbers** **• the ideas of a famous mathematician, which we followed up by seeing how their maths understandings are used today** **• using our maths knowledge and strategies to solve problems in game situations.**
 * Each week we explored**

__Week 1__ **Roman Numerals** I =1 II =2 III =3 IV =4 V =5 VI =6 VII =7 VIII =8 IX =9 X =10 L =50 C =100 D =500 M =1000 Some problems with the Roman Number System are • it doesn’t include zero •it’s unwieldy to work with compared with the Decimal System, as it doesn’t have place value • t here has never been a universally accepted set of rules for Roman numerals e.g. 1999 could be written as MDCCCCLXXXXVIIII, MCMXCIX, or MIM.

**Enter Leonardo Fibonacci** Compared with the Roman Numeral System previously used in Europe, the Hindi Arabic Number System introduced by Italian mathematician Leonardo Fibonacci (born 1175) was much easier to use add, subtract, multiply, divide. We still use the numbers he introduced: 0 1 2 3 4 5 6 7 8 9.

**Fibonacci Numbers** Leonardo Fibonacci studied the number patterns of breeding rabbits, male honeybees and the branching of plants like the sneezewort. The pattern he discovered is now called the “Fibonacci Numbers.” 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… keep adding the last 2 numbers together to find the next number in the sequence. Fibonacci Numbers are found in lots of places.

**Fibonacci’s Golden Spiral** We used graph paper to make tiles of Fibonacci Numbers, then we used a compass to make arcs across each square, ending up with a spiral which is found in many places in nature, including nautilus shells, pinecones and sunflowers.

**Fibonacci’s Golden Number** If you divide one of the bigger Fibonacci numbers by the one before it, you arrive at this very special number. Try these: 610 divided by 377 377 divided by 233 233 divided by 144 This is found in shapes and designs in nature. It’s also found in many shapes and designs made by people. They “feel right”.

Measure the length of the room. Measure the width of the room. Divide the length by the width... If it’s a room that “feels right”, often it works out to Fibonacci’s Golden Number of 1.6180

There are lots of internet references to Fibonacci. Check out this youtube clip: **Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]**

__Week 2__ **Square Numbers and Square Root of Numbers** We looked at the area made by squares of different unit lengths, starting with 1 and going up to 13. 12 is the same as 1 x 1, or the area of a square with sides that are 1 unit in length. 132 is the same as 13 x 13, or the area of a square with sides that are 13 units in length.

Square roots help us find the length of the sides of a square, when we know the area. There’s a square root function key on many calculators.

**Pythagoras** He was a philosopher, mathematician and musician who lived in Greece, born around 565BC. He had lots of followers who studied under him. The motto of his “school” was “All is Number.” It was a long time ago and there are lots of stories about him, written after he died, so it’s hard to tell what’s true! Pythagoras is famous now for his Pythagorean Theorem and his contribution to tuning musical instruments.

**Pythagoras’ Theorem** You can work out the hypotenuse or length of a right angle triangle using his idea or theorem.

**Pythagoras’ Ratios** We used 6 jars to measure out the amounts of water below.
 * Jar || Water  || Relationship  || Pythagorean Ratio ||
 * 1 || 360 ml  || 360/180  || 2 to 1  ||
 * 2 || 300 ml  || 300/180  || 5 to 3  ||
 * 3 || 270 ml  || 270/180  || 3 to 2  ||
 * 4 || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">240 ml  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">240/180  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">4 to 3  ||
 * <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">5 || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">225 ml  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">225/180  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">5 to 4  ||
 * <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">6 || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">180 ml  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">180/180  || <span style="color: #2f1a14; display: block; font-family: 'Comic Sans MS'; font-size: 14pt; text-align: center;">1 to 1  ||

We recognized the notes made when you hit the jars with a pen or stick. E, F#, G, A, B, D are the 6 note scale found by Pythagoras and used for centuries, until the 8 note scale was discovered.

**Fractals** “Fractals” comes from the same root word as “fractions.” Fractals are a repeating shape or pattern that gets smaller and smaller. You find them in nature in lots of places where you find Fibonacci Numbers and fractals are used in computer graphics and animation work. Pythagorean Fractals are based on squares and right angle triangles, in a repeating pattern that gets smaller and smaller.

There are lots of internet references to Pythagoras.

Check out this youtube clip: