For cartesian plans, for functions, why are x and y the letters we use as variables?
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That’s an interesting question. It seems like it goes back to Renees Descartes. Among other things, Renees Descartes was a mathematician who did a lot of work with algebra and geometry. He invented the concept of cartesian coordinates, where you plot things on an X and Y axis and he came up the notation for powers where the number goes slightly above the other number: x^2 . Anyway, he preferred using x, y and z for unknown values when he did algebra, and mathematicians just stuck with that for hundreds of years.
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If I recall correctly, X is used as the default unknown quantity in algebra, because some Arabic word, when translated into Spanish sounds a bit like X.
As for y. It’s next in the alphabet.
I’m sure someone will have a more detailed answer for you, but I’m sure you can find the details with a Google search from here
Descartes was the mathematician who proposed and formalized the coordinate system that was subsequently named after him (cartesian).
He used the first letters of the alphabet to signify known quantities and the last few letters to signify unknowns. The tradition started from there. (this might be apocryphal since x and y were probably already used before his time)
Very generally speaking, this developed into an informal ‘system’.
a,b,c are used for scalar (or real number) constants. (e isn’t typically used because it refers to euler’s constant. In physics, c, is usually reserved for the speed of light)
f,g,h are used for function names typically. In kinematics physics, g is usually reserved for the acceleration due to earth’s gravity
i,j (and sometimes k) is used as subscripts, indices or with a “hat” to denote unit vectors.
k,m,n, (mostly m and n) are used to denote integer constants or integer unknowns.
p,q,r are also commonly used to represent vector unknowns. (a,b,c are usually scalar constants or unknowns)
s,v and t are used in physics typically to denote displacement, velocity and time. (In kinematics physics, u is used for initial velocity)
u,v,w are also quite often used for vector variables.
x, y, z are used for variables. z is commonly used to represent complex number variables. (so if a problem states z^3 =1, you should assume that z refers to complex number solutions and responding with z = 1 is incomplete or incorrect.)
l and o are rarely used because it too easy to mistake it for “1” and “0”
Algebra was bought to Europe by muslims when they invaded the Iberian peninsula. Back then, they called their unknowns “the thing”, witch in arabic is “say”. When traslated into latin form in Spain, it was written xei and, from there, x to name an unknown. Y, z to follow after x in modern alphabets.
I think 1 is a commonality (mid point un equated or a point of reverse engineering towards a commonality) variable and the other an end result of the accumulation of variables.
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