Spouge's approximation is a really smart way of guessing (or approximating) the value of a math concept called the gamma function.
The gamma function is a special type of function that can tell us the area under a curve. It's kind of like a ruler that lets us measure how much of the space under a curve is filled up.
Now, the gamma function can be really hard to calculate because it involves a lot of complicated math. But Spouge, a smart mathematician, figured out a simpler way to guess its value using a formula he came up with.
His formula is like a recipe that helps us mix together a bunch of smaller numbers to get an estimate for the gamma function. It's kind of like when we're making cookies and we add a little bit of flour, sugar, and butter together to create something delicious.
Spouge's formula isn't perfect, but it's pretty good at giving us a rough idea of what the gamma function is. And sometimes, that's all we need!