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Here are a **couple** of **pairs** of **deuces**:

**CONTINUED FRACTIONS:** consider this fraction:

If we continue the process indefinitely, what answer do we get? The answer is $-1+\sqrt 3$ (which is **irrational** i.e. cannot be written as a integer fraction !). To see this, call the continued fraction $x$ and observe that $\frac{2}{2+x}$ gives the same continued fraction as the original $x$. Now rearrange $\frac{2}{2+x}=x$ and solve the resulting quadratic (degree TWO) equation.

What number would this continued fraction give? $\frac{3}{3+\frac{3}{3+…}}$

**TWO** is the wheels on a **bi**cycle, the ends of a **di**ameter or a **di**agonal, and two is a duplicitous timer. We need two co-ordinates to find our place on a map in flatland; even at sea on a sphere just two numbers – **latitude** and **longitude **– tell us where we are. Not only the Earth’s surface but any plane in fact has two ‘**dimensions**‘ (a curve has one and a point zero dimensions).

The number two is in a sense indifferent to **ADDITION**, **MULTIPLICATION **and **EXPONENTIATION**, since 2 plus 2 = 2 times 2 = 2^2; swap three for two and it’s no longer true.

$2+2=2\times 2=2^2$

**BINARY CODES: **these are codes made of two ingredients, such as Braille (raised and flush), Morse (dots and dashes), Bar Codes (black and white stripes), QR codes (black and white squares) and of course Base two (0’s and 1’s).

**HERE’S A DILEMMA:** there are of course TWO answers to this “missing word” puzzle: can you find them both?

Read all about NUMBER ONE: we like you too;

Number two: we salute you!

- STAR POLYGONS
- CIRCULAR REASONING: TOP TIPS FOR USING A COMPASS
- TRIANGULAR NUMBERS AND PYTHAGOREAN TRIPLES – A SURPRISING RELATIONSHIP
- FUN WITH OCTAGONS
- ADVENTURES IN THE FOURTH DIMENSION
- STRICTLY COME COUNTING
- WHY ARE THE STONES AT GIANTS CAUSEWAY HEXAGONAL?
- WHAT’S SPECIAL ABOUT THE NUMBER TWO?
- WHAT’S SPECIAL ABOUT THE NUMBER ONE?
- DOGARITHMS
- HOW MOST PEOPLE CAN BE “BETTER THAN AVERAGE”!
- WHY IS x USED FOR THE UNKNOWN IN ALGEBRA?
- 5 REASONS MATHS IS THE MOST IMPORTANT SUBJECT
- PARALLAX, PENTAPRISMS AND PHOTOGRAPHY
- 6 WAYS TO MAKE MATHS FUN
- THE TEN COMMANDMENTS OF MATHS
- SUPERSTARS OF MATHS – JOHN VENN
- SUPERSTARS OF MATHS – RENE DESCARTES
- HEXAHEDRA AND OTHER “HEX” WORDS
- WHICH IS BETTER: METRIC OR IMPERIAL?
- HOW MANY GIFTS IN TOTAL IN “THE TWELVE DAYS OF CHRISTMAS”?
- FUN WITH THE NEW POLYMER FIVE POUND NOTE
- HOUSE OF MATHS MAKES THE NATIONAL NEWS!
- FACTORS AND MULTIPLES
- SUPERSTARS OF MATHS – ISAAC NEWTON
- SUPERSTARS OF MATHS – LEONHARD EULER
- WHAT IS THE POINT OF ALGEBRA?