# What Is the Circle Constant Pi?

In the field of geometry you have learned about so far, you have studied circles and therefore used the number $3.14$ a bit out of the blue. But $3.14$ is not taken out of thin air. It is a rounding of the number $\pi$ (pronounced “pie”). In the box below, you will see $\pi$ with a few more decimal places.

$\pi$ is one of the strangest, most interesting numbers we have. But what exactly is $\pi$, and where did it come from? The number $\pi$ is a ratio. It is the ratio of the circumference to the diameter of a circle. What’s so incredible is that no matter which circle you choose—huge, or very small— the ratio between the circumference and the diameter of the circle will always be exactly the same: precisely $\pi$.

$\pi$ is an irrational number. That is, $\pi$ cannot be written as a fraction of integers. $\pi$ has infinitely many decimals that do not follow any pattern. The decimals in the number seem to have been thrown out at random.

### $\pi$with261Decimals

$\begin{array}{llll}\hfill & 3.141\phantom{\rule{0.17em}{0ex}}592\phantom{\rule{0.17em}{0ex}}653\phantom{\rule{0.17em}{0ex}}589\phantom{\rule{0.17em}{0ex}}793\phantom{\rule{0.17em}{0ex}}238\phantom{\rule{0.17em}{0ex}}462\phantom{\rule{0.17em}{0ex}}643\phantom{\rule{0.17em}{0ex}}383\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}279\phantom{\rule{0.17em}{0ex}}502\phantom{\rule{0.17em}{0ex}}884\phantom{\rule{0.17em}{0ex}}197\phantom{\rule{0.17em}{0ex}}169\phantom{\rule{0.17em}{0ex}}399\phantom{\rule{0.17em}{0ex}}375\phantom{\rule{0.17em}{0ex}}105\phantom{\rule{0.17em}{0ex}}820\phantom{\rule{0.17em}{0ex}}974\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}944\phantom{\rule{0.17em}{0ex}}592\phantom{\rule{0.17em}{0ex}}307\phantom{\rule{0.17em}{0ex}}816\phantom{\rule{0.17em}{0ex}}406\phantom{\rule{0.17em}{0ex}}286\phantom{\rule{0.17em}{0ex}}208\phantom{\rule{0.17em}{0ex}}998\phantom{\rule{0.17em}{0ex}}628\phantom{\rule{0.17em}{0ex}}034\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}825\phantom{\rule{0.17em}{0ex}}342\phantom{\rule{0.17em}{0ex}}117\phantom{\rule{0.17em}{0ex}}067\phantom{\rule{0.17em}{0ex}}982\phantom{\rule{0.17em}{0ex}}148\phantom{\rule{0.17em}{0ex}}086\phantom{\rule{0.17em}{0ex}}513\phantom{\rule{0.17em}{0ex}}282\phantom{\rule{0.17em}{0ex}}306\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}647\phantom{\rule{0.17em}{0ex}}093\phantom{\rule{0.17em}{0ex}}844\phantom{\rule{0.17em}{0ex}}609\phantom{\rule{0.17em}{0ex}}550\phantom{\rule{0.17em}{0ex}}582\phantom{\rule{0.17em}{0ex}}231\phantom{\rule{0.17em}{0ex}}725\phantom{\rule{0.17em}{0ex}}359\phantom{\rule{0.17em}{0ex}}408\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}128\phantom{\rule{0.17em}{0ex}}481\phantom{\rule{0.17em}{0ex}}117\phantom{\rule{0.17em}{0ex}}450\phantom{\rule{0.17em}{0ex}}284\phantom{\rule{0.17em}{0ex}}102\phantom{\rule{0.17em}{0ex}}701\phantom{\rule{0.17em}{0ex}}938\phantom{\rule{0.17em}{0ex}}521\phantom{\rule{0.17em}{0ex}}105\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}559\phantom{\rule{0.17em}{0ex}}644\phantom{\rule{0.17em}{0ex}}622\phantom{\rule{0.17em}{0ex}}948\phantom{\rule{0.17em}{0ex}}954\phantom{\rule{0.17em}{0ex}}930\phantom{\rule{0.17em}{0ex}}381\phantom{\rule{0.17em}{0ex}}964\phantom{\rule{0.17em}{0ex}}428\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}810\phantom{\rule{0.17em}{0ex}}975\phantom{\rule{0.17em}{0ex}}665\phantom{\rule{0.17em}{0ex}}933\phantom{\rule{0.17em}{0ex}}446\phantom{\rule{0.17em}{0ex}}128\phantom{\rule{0.17em}{0ex}}475\phantom{\rule{0.17em}{0ex}}648\phantom{\rule{0.17em}{0ex}}233\phantom{\rule{0.17em}{0ex}}786\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{3,}783\phantom{\rule{0.17em}{0ex}}165\phantom{\rule{0.17em}{0ex}}271\phantom{\rule{0.17em}{0ex}}201\phantom{\rule{0.17em}{0ex}}909\phantom{\rule{0.17em}{0ex}}145\phantom{\rule{0.17em}{0ex}}648\phantom{\rule{0.17em}{0ex}}566\phantom{\rule{0.17em}{0ex}}923\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Rule

### Definitionof$\pi$

 $\pi =\frac{\text{circumference}}{\text{diameter}}$

The figure below shows the different formulas you get by solving the expression in the box for the various variables. You do not need to remember these, but learn how to solve the equation. Regardless, the most important thing to remember is that the number $\pi$, is defined as the ratio of the circumference to the diameter of a circle.