noun
base (logarithm, exponential, number system); radix
Technical term in mathematics for the base of a logarithm, exponential function, or number system.
10を底とする対数を常用対数という。
A logarithm with base 10 is called a common logarithm.
noun
base (triangle, cone, cylinder, etc.)
Geometric term for the base of a shape, such as the bottom side of a triangle or the circular face of a cone or cylinder.
三角形の底辺の長さを測る。
Measure the length of the base of the triangle.
noun
Rare, somewhat literary use to indicate a category, nature, or degree. More commonly expressed with 種類, 程度, or 性質 in modern Japanese.
この底の話は初めて聞いた。
I've never heard this kind of story before.
基数 is the more common term for 'radix' or 'base' in number systems, while 底 is used in logarithmic and exponential contexts.
底面 specifically refers to the bottom face of a solid, whereas 底 can refer to the base of any geometric figure.
The kanji 底 originally means 'bottom' or 'base'. The reading てい is the on'yomi, used in technical and abstract contexts. The exact historical derivation of the mathematical senses is uncertain, but they are extensions of the core meaning of 'base'.