My own Heron's formula

While I was studying something today, I encountered the famous Heron's formula by chance.

Though I have learned it since maybe around 20 years ago, I don't like it's looking due to the unbalance coming from the single 's' against the other 3 's' with subtraction.

So I've just come up with the idea to deduct my own formula only with the three lengths of the triangle sides (x,y & z).
Eventually I've reached the certain result as follows.


To me, it looks more beautiful in respect of its conformity.
Furthermore it's easy to memorize.

Then I just wanted to know how they look in Grapher on MacMini, so I created the animation with the following equation.


Here is my first uploaded movie on youtube showing the result.
This animation indicates any arbitrary point on the surface gives the three sides of a triangle whose area is 1. Impressive.