### Pi Kappa Phi Contains Two Irrational Math Constants

TempeHiker found Pi and Phi at the 2007 Parada del Sol parade in Scottsdale.

Pi `(π)` is the 16th letter of the Greek alphabet and it has the Greek numerical value of 80.

Kappa `(K)` is the 10th letter of the Greek alphabet and it has the Greek numerical value of 20.

Phi `(φ)` is the 21st letter of the Greek alphabet and it has the Greek numerical value of 500.

Pi Kappa Phi in symbols: πkφ

In math world, Pi and Phi are irrational constants having the values `3.1416...` and `1.618...`, respectively. Phi is called the "golden ratio." Kappa is not a number in math world.

Pi and Phi can be crudely approximated as follows.

```   Pi  = 3.14159265...
Phi = 1.61803399...

Pi = 22/7 = 3.14285714   or   666/212 = 3.14150943

Phi = (1 + sqrt(5))/2 = 1.61803399  or  610/377 = 1.61803713
```

A Phi related sequence...

```   1/1  2/1  3/2  5/3  8/5  13/8  21/13  34/21  55/34
89/55  144/89  233/144  377/233  610/377

1/1     = 1.0
2/1     = 2.0
5/3     = 1.66666667
8/5     = 1.6
13/8    = 1.625
21/13   = 1.61538461
34/21   = 1.61904761
55/34   = 1.61764705
89/55   = 1.61818181
144/89  = 1.61797752
233/144 = 1.61805555
377/233 = 1.61802575
610/377 = 1.61803713
```
##### Exercises
1. Using Greek numerical values, evaluate: `Pi + K + Phi = _______`.

2. Using the mathematical constants: `Pi + Phi = ______________`. [round answer to the nearest millionth]

3. Find the next fraction in the aforementioned "Phi related sequence."

##### More... About Pi Kappa Phi

The Wikipedia says: "Pi Kappa Phi is a national social fraternity that was founded in the spirit of 'nu phi,' meaning non-fraternity, in 1904 in Charleston, South Carolina."

Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 26 February 2007