Calorie

a unit of quantity of heat defined as that heat needed to raise the temperature of one gram of water through 1°C. Nowadays, it has largely been replaced by the JOULE (1 calorie = 4.186 joules).

Taken from Dictionary of Science

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The calorie is a pre-SI metric unit of energy. The unit was first defined by Professor Nicolas Clément in 1824 as a unit of heat. This definition entered French and English dictionaries between 1841 and 1867. In most fields its use is archaic, having been replaced by the SI unit of energy, the joule. However, in many countries it remains in common use as a unit of food energy. The kilocalorie per mole remains in use in computational chemistry and molecular spectroscopy.

Definitions vary but are all based on the specific heat capacity of water. The gram calorie, approximately 4.2 J, is based on one gram of water. The kilogram calorie, equal to one thousand gram calories, is based on one kilogram of water. In the context of nutrition, and especially food labelling, a larger unit is used and referred to interchangeably by the terms calorie (or Calorie) and kilocalorie.

Taken from Wikipedia

Factorial

the multiplication of a series of consecutive numbers from I to n inclusive, where n is a whole number. Thus, factorial 5, written as 5! = 1 x 2 x 3 x 4 x 5 = 120. Factorials of much larger numbers are not usually defined.

Taken from Dictionary of Science

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In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

and

The notation n! was introduced by Christian Kramp in 1808.

The factorial function can also be defined for non-integer values, which involves more advanced mathematics, especially mathematical analysis.

Taken from Wikipedia

Tangent

a function of an angle in a right-angled triangle, defined as the ratio of the side opposite the angle to the length of the side adjacent to it. Also, in geometry, a straight line that just touches the circumference of a circle.

Taken from Dictionary of Science

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In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to space curves and curves in n-dimensional Euclidean space.

Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

The word "tangent" comes from the Latin tangere, meaning "to touch".

Taken from Wikipedia