What is algebra used for?

Answer 1

Algebra (from Mohammed ibn-Musa Khwarizimi's book Al-jabr wa'l muqabalah), allows arithmetic to be performed with pronumerals ("variables") instead of fixed numbers.

2*3=6 is arithmetic - the "2*3" part can only ever give one correct answer, "6".

2*a=b is algebra.

Whatever value we substute for "a", the answer ("b") must be twice that value, so:

If a = 3, b = 6, if a = 10, b = 20, if a = 1/4, b = 1/2, if a = -7, b = -14, and so on.

Algebra is most often seen in expressions (equations or formulae) that state general mathematical principles, and can be used to give results for wide ranges of values.

Newton's Law of Gravitation, F = G*M1*M2/(d2) is a famous example, showing the attractive force between two objects.

If you know the two masses (M1, M2), and the distance between them, and you know the gravitational constant (G), you can work out the attractive force between any two masses, even if they are separated by great distances such as the Sun and planet Neptune.

Be aware the Newton's formula is "pretty accurate" (good enough for the Apollo missions to the moon!), but that recent measurements point to some refinement being needed.

Science, after all, is not an exact science!

Some expressions may be undefined for particular values. It is not possible to divide any number by zero, so values that force an attempt to divide by zero cannot be solved.

The result of division by zero *is not* "infinity". There just is no answer.

An example: the period of a pendulum is 2*pi*sqrt(l/g), where pi is approx 3.14159, l is the pendulum's length, and g is the local gravitational attraction.

If g is zero, the formula is undefined, with no answer.

Intuitively, the pendulum is not going to swing in the absence of any restoring force! and then you have to go take a dump on the grave of your friends dead relatives