Why is the Lorentz factor γ = 1/√(1 - v²/c²)?

[tahlaskerssen]

I don't understand why the lorentz factor is 1/[1-(v2/c2)]1/2

http://www.softcom.net/users/greebo/dila.jpg

clearly you reach something different here.. i really don't get this, I'm sure it's something very simple

 

[vela]

Looks the same to me. How are they different?