Greek and latin letters in maths

1. 3rd High School of
Polichni

2.  During human history, symbols appeared for many different
reasons in order to help communication, art and expression.
 Today symbols and symbolic representation exist in every
human activity replacing sometimes verbal communication
and they often create new communication and behavior
codes.
 In maths, the use of symbols for written math expressions
appeared from the early days and now mathematic
communication is impossible without knowing the symbols
that are used.

3.  In math education symbols play an important role both to
teaching and learning
 Mathematical symbolism is a powerful communication tool in
every math conversation.
 Teachers can easily use symbolism in syntactical and semantic
level
 Students usually consider math symbolism as a new language
in which they are forced to translate the expressions of the
language that they speak and the opposite.
 Great knowledge of math symbolism assists to a successful
learning.

4. The number π is a mathematical constant.
Originally defined as the ratio of a circle's
circumference to its diameter, it now has
various equivalent definitions and appears in
many formulas in all areas of mathematics
and physics. It is approximately equal to
3.14159. It has been represented by the
Greek letter "π" since the mid-18th century,
though it is also sometimes spelled out as
"pi" and derived from the first letter of the
Greek word perimetros, meaning
circumference.

5. The number e is a mathematical constant,
approximately equal to 2.71828, which appears in many
different settings throughout mathematics. It was
discovered by the Swiss mathematician Jacob Bernoulli
while studying compound interest. The number e can
also be calculated as the sum of the infinite series.
Also called Euler's number after the Swiss
mathematician Leonhard Euler the Euler–Mascheroni
constant, which is sometimes called simply Euler's
constant. Occasionally, the number e is termed Napier's
constant, but Euler's choice of the symbol e is said to
have been retained in his honor.

6. The imaginary unit or unit
imaginary number (i) is a
solution to the quadratic
equation x2 + 1= 0.
Although there is no real
number with this property, i
can be used to extend the
real numbers to what are
called complex numbers,
using addition and
multiplication. A simple
example of the use of i in a
complex number is 2 + 3i.

7. In mathematics, summation (capital Greek sigma symbol: Σ) is
the addition of a sequence of numbers; the result is their sum or
total. If numbers are added sequentially from left to right, any
intermediate result is a partial sum, prefix sum, or running total
of the summation. The symbol Σ is come from the Greek word
synolo whicn means summation.

8. The product of a sequence of
terms can be written with the
product symbol, which derives
from the capital letter Π (Pi) in
the Greek alphabet. Capital Pi
comes from the Greek word
“Pollaplasiasmos” which means
multiplication. Multiplication is
one of the four elementary
mathematical operations of
arithmetic; with the others being
addition, subtraction and
division.

9. It is a division of a straight
segment AB into two
segments, a large α and a
small β, so that it applies:
α/β= α+β/α=1,618. The
above is internationally
symbolized by the Greek letter
"φ”, which is the first letter of
the name of sculptor Pheidias,
who used the Golden Section
in his works.

10. The number γ has not been proved algebraic or transcendental. In
fact, it is not even known whether γ is irrational. Continued fraction
analysis reveals that if γ is rational, its denominator must be greater
than 10242080. The ubiquity of γ revealed by the large number of
equations below makes the irrationality of γ a major open question in
mathematics.
The constant first appeared in a 1734 paper by the Swiss
mathematician Leonhard Euler, titled De Progressionibus harmonicis
observationes (Eneström Index 43). Euler used the notations C and O
for the constant. In 1790, Italian mathematician Lorenzo Mascheroni
used the notations A and a for the constant. The notation γ appears
nowhere in the writings of either Euler or Mascheroni, and was
chosen at a later time perhaps because of the constant's connection
to the gamma function.

11. In mathematics, the natural numbers
are those used for counting and
ordering. Some definitions, including
the standard ISO 80000-2 begin the
natural numbers with 0,
corresponding to the non-negative
integers 0, 1, 2, 3, …, whereas
others start with 1, corresponding to
the positive integers 1, 2, 3, ….
Texts that exclude zero from the
natural numbers sometimes refer to
the natural numbers together with
zero as the whole numbers, but in
other writings, that term is used
instead for the integers.
Mathematicians use N or ℕ to refer
to the set of all natural numbers.

12. The negative of a positive integer is
defined as a number that produces 0
when it is added to the corresponding
positive integer. Negative numbers are
usually written with a negative sign (a
minus sign). As an example, the
negative of 7 is written −7, and 7 +
(−7) = 0. When the set of negative
numbers is combined with the set of
natural numbers (including 0), the result
is defined as the set of integers {Z}.
Here the letter Z comes from German
Zahl, meaning 'number'. The set of
integers forms a ring with the
operations addition and multiplication.

13. A rational number is a number that
can be expressed as a fraction with
an integer numerator and a
positive integer denominator.
Negative denominators are
allowed, but are commonly
avoided, as every rational number
is equal to a fraction with positive
denominator. Fractions are written
as two integers, the numerator and
the denominator, with a dividing
bar between them. The symbol for
the rational numbers is Q (for
quotient).

14. Moving to a greater level of
abstraction, the real numbers can be
extended to the complex numbers.
This set of numbers arose
historically from trying to find closed
formulas for the roots of cubic and
quadratic polynomials. This led to
expressions involving the square
roots of negative numbers, and
eventually to the definition of a new
number: a square root of −1,
denoted by i, a symbol assigned by
Leonhard Euler, and called the
imaginary unit. The number is called
a Gaussian integer. The symbol for
the complex numbers is C.

15. Every real number is either
rational or indiscriminate. Each
real number corresponds to a
point on the line of numbers.
Also, the real numbers have a
significant but extremely
technical property called the
minimum upper barrier. The
symbol for the real numbers is
R.

16.  As Alfred North Whitehead says , the notation in math can
<<relieve the brain from any unnecessary wοrk. A good
notation releases in order to concentrate on more advanced
problems and actually increases the intellectual power of
man>>

17.  IAKOVAKI CHRYSOULA
 KATSAROS EVANGELOS
 MOUTIKAS ANGELOS
 SARAFIS CHRISTOS