Focal Points- Extending/Retracting Barrel?

So I was looking at some lenses on youtube and I had noticed (this has been for a long time now) that, and I don't know if this is specific to Nikon, lenses from Nikon retract from smallest focal point but then at a certain point it extends again, and its pretty much at some halfway point in the lens. For example, a 24-70 2.8G from Nikon is fully retracted at 50mm, but fully extended at 24mm, even though in the viewfinder you would go "back", and on my kit lens it was the same, at 18mm it was extend but somewhere between 24-35 it would extend again but not as far.

So is there some mathematical/scientific reason to this, I don't look to much into lens construction and directing light but this does interest me so you can be as technical as you want

Yeah, it's to do with the construction of the lens. Two of the glass elements in the lens need to be further away from each other to have a wider field of view hence the lens is fully extended at 24mm.

It's all to do with lens construction, the placement of the pieces of glass and the degree on the convex and concave glass elements.