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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!

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