Numerical Techniques: Part Two

So today I expanded on the programs I made yesterday. Now it can handle a sphere, an ellipsoid, or torus, and ultimately finds what is called the "intrinsic curvature" of the object in terms of a particular distortion (currently involving just increasing the radius, essentially, but can be modified for any kind of distorting). I have no idea what this curvature actually represents, but apparently my programs calculate it right! That's always good.

Differential Geometry

So today I read up on this titular subject, and came to the conclusion that it is the possibly cannibis-induced lovechild of set theory and vector calculus. For those unfamiliar with the subjects, they are two very core fields in mathematics. I know many people who are good at one and only one (myself included); I know of none adept at both.

The following words have defined mathematical meanings that I was completely unaware of before today:

• Patch
• Umbilical
• Monkey saddle
• Maximal
• Compact
• Pullback
• Pushout
• Categorical dual
  
• Bundle
• Fibre product
• Functor

And no, I am not exaggerating in any way. Each and every one of these terms is related in some manner to differential geometry, I have discovered them all in my reading.

Update: I reworded things a little, as previously this entry sounded far more harshly than I intended.