Wavelength

(λ) the distance between two similar and consecutive points on a wave, which have exactly the same displacement value from the rest position (that is, the same amplitude). An example would be the distance between two crests (maximum displacement) or two troughs (maximum displacement). Wavelength is a measure of distance and hence has units of metres (m).

Taken from Dictionary of Science

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In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

Examples of wave-like phenomena are sound waves, light, and water waves. A sound wave is a periodic variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are periodic variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary periodically in both lattice position and time.

Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength.

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