Pi and phi are different Greek letters. We have been discussing pi, which expresses the ratio between the circumference and the diameter of a circle. If the diameter is 1.00, then the circumference is pi (3.14159...)
phi is a different letter and stands for different values in several fields:
The lower-case letter \varphi \, (or often its variant, \phi \,) is often used to represent the following:
* The golden ratio \tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots in mathematics, art, and architecture.
* Euler's totient function ?(n) in number theory; also called Euler's phi function.
* In algebra, group or ring homomorphisms
* In probability theory, ?(x) = (2?)?½e?x2/2 is the probability density function of the normal distribution.
* In probability theory, ?X(t) = E[?eitX?] is the characteristic function of a random variable X.
* An angle, typically the second angle mentioned, after ? (theta). Especially:
o The argument of a complex number.
o The phase of a wave in signal processing.
o In spherical coordinates, mathematicians usually refer to phi as the polar angle (from the z-axis). The convention in physics is to use phi as the azimuthal angle (from the x-axis).
o One of the dihedral angles in the backbones of proteins.
o Internal or effective angle of friction.
* Electric potential in physics.
* The work function in electronics.
* A shorthand representation for an aromatic functional group in organic chemistry.
* The fugacity coefficient in thermodynamics.
* The ratio of free energy destabilizations of protein mutants in phi value analysis.
* In cartography and navigation, latitude.
* In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
* A sentence in first-order logic.
* Porosity in geology and hydrology.
* Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
* The symbol for a voiceless bilabial fricative in the International Phonetic Alphabet (using the straight line variant character)
* In economics, this is usually an additive term.[clarification needed]
* In flight dynamics, the roll angle.
The upper-case letter ? is used as a symbol for:
* The golden ratio conjugate ?0.618... in mathematics.
* The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
* The cumulative distribution function of the normal distribution in mathematics and statistics.
* Philosophy.[why?]
* The number of phases in a power system in electrical engineering, for example 1? for single phase, 3? for three phase.
* A common symbol for the parametrization of a surface in vector calculus.
* In Lacanian algebra, ? stands for the imaginary phallus and also represents phallic signification. -? stands in for castration
I am not familiar Lacanian algebra, but it sounds rather intriguing.
