some geometry . more modern then plato. b.c. geometry. terms.

measure theory
Measure theory investigates the conditions under which integration can
take place.
It considers various ways in which the "size" of a set can be estimated.
differential equation
A differential equation is an equation involving the first or higher
derivatives of the function to be solved for.
If the equation only involves first derivatives it is called an equation
of order one, and so on.
If only n-th powers of the derivatives are involved, the equation is
said to have degree n. Equations of degree one are called linear.
Equations in only one variable are called ordinary differential
equations to distinguish them from partial differential equations.
partial differential equation
A partial differential equation is an equation involving derivatives
with respect to more than one variable.
Many of the equations used to model the physics of the real world are
partial differential equations.
gymnasium
A gymnasium is a senior secondary school in Germany and certain other
countries of mainland Europe.
number theory
Number theory is the study of the properties of the natural numbers N.
It includes such topics as prime numbers, including the prime number
theorem, quadratic reciprocity, quadratic forms, diophantine
approximation and diophantine equations, algebraic number fields,
Fermat's last theorem and the methods developed to prove it.
prime number theorem
The Prime Number Theorem states that
The number of primes n tends to as fast as n/loge n.
quadratic reciprocity
The Law of Quadratic Reciprocity gives the conditions for a prime p to
be a quadratic residue modulo a prime q in terms of whether of not q is
a quadratic residue modulo p.
quadratic form
A quadratic form is a general expression with a second order terms.
In two variables it is usually written:
ax2+ 2hxy + by2 + 2gx + 2fy + c.
diophantine approximation
Diophantine approximation is approximating real numbers by rationals
(ratios of integers).
diophantine equation
A Diophantine equation is one which is to be solved for integer
solutions only.
algebraic number field
An algebraic number field is a subfield of R or C which contains the
rational numbers Q as well as the roots of some polynomial with rational
coefficients.
For example, the field written Q (2) is the set of real numbers {a + b2
| a, b are rationals}. This contains the roots of the equation x2 - 2 =
0.
Fermat's last theorem
Fermat's last theorem (so called because it was the last of the results
which Fermat claimed and which had not been proved) states that if n > 2
then the equation xn + yn = zn has no positive integer solutions.
quadratic residue
An integer m is a quadratic residue modulo n if m = r2 modulo n for some
r.
Other numbers are called quadratic non-residues.
modulo
We say that numbers m and n are equal modulo p, if p divides exactly
into m - n.
modulo
We say that numbers m and n are equal modulo p, if p divides exactly
into m - n.