Maths history

1. History of
Mathematics

2. What is mathematics?
 Mathematics is the study of relationships among quantities, magnitudes and
properties and of logical operations used to derive quantities, magnitudes and
unknown properties.
 Mathematics is as old as humanity itself.
 The advanced, organized mathematics were developed in the third
millennium BC in Babylon and Egypt, which were dominated by arithmetic,
with some interest in geometric measurements and calculations.

3. Egyptians in mathematics
 The first Egyptian books show a decimal number system with different
symbols for powers of 10, similar to Roman numerals. Numbers were
represented by writing 1 as many times as units had the figure given, 10, as
often as dozens had, and so on. To add, were added in different sections
units, tens, hundreds ... of each number to get the right result. Was based on
the successive multiplication and division duplication was the reverse process.
 The Egyptians used sums of fractions unit (D), together with the fraction, to
express all fractions. In geometry found rules to calculate the area of
triangles, rectangles and trapezoids, and volume figures as cuboids, cylinders
and pyramids. To calculate the area of a circle, they used a square of side ð
diameter of the circle, close value to that obtained using pi 3.1416.

4. The Babylonians in mathematics
 Babylonian tablets carved with several wedges (wedge); It is
representing a simple wedge 1 and as represented by arrow 10. Any
number under 59 were formed by these symbols using an additive
process, as did the Egyptians and Romans. But 60, was represented by
the symbol 1, and thereafter, the value of a symbol was given by its
position in the full amount. This way of expressing numbers, was
extended to the representation of fractions. Later this system was
called sexagesimal.

5. Tablet with geometric motifs

6. Egyptian tables
The Egyptians used fractions
with numerator only one (1),
such as 1/3, 1/7, 1/15, 1/47
Render papyrus contains a table
of conversion of parts of the
unit to these fractions. It is
equivalent to more than 3000
years of our multiplication
tables, only to work with
fractions.
According to Herodotus the Egyptians are the parents of
geometry, but also had a sophisticated numbering system
that allowed them to work with fractions of a special
form because the numerator was always unity. In the
papyri of Rinda and Moscow, a collection of over 100
Egyptian mathematical problems appear. His numbering
system was base-ten. The symbols to represent powers
of 10 were:

7. Pythagoras
The Pythagorean theorem has lots of
demonstrations, even Mr Scott Loomis
gathered information and published in the
early twentieth century that had 367
demonstrations, although there is
obviously room for error. The Pythagorean
Theorem is as follows:
24 24 18 18

8. Roman numerals
 Numbering system of the Romans, the problem is that it is not a good tool for
the calculation, since it uses letters of the alphabet to represent numbers and
is not positional, ie each symbol always worth the same, no matter where it is
placed. The figures are used are: I, V, X, L, C, D, M. The system is based on
the sum of the symbols. Except in a smaller number sign precedes a larger
one, then subtraction

9. GAUSS
 Gauss is one of the geniuses in the history of mathematics. His contributions
were incredible and because of this, some of them waited more than a
century to be accepted.
 Gauss's contributions were many who became invaluable; some of them are
the theory of numbers, Astronomy, Magnetism, Geometry, Analysis. The vast
majority, if not all discoveries in the nineteenth century, due to Gauss:

10. More gauss
 Disquisiciones arithmetic, written in 1799 and published in 1801, was the
masterpiece of number theory at the time, which placed Gauss at the summit
of mathematics, at age 24. Article 293 of the fifth section demonstrates that
all Gauss integer is the sum of at most three triangular numbers and four
squares. N = d d d d
 His greatest achievement was the fact that he built the regular polygon of 17
sides, which no one had previously achieved.
 But that was not enough, so he devoted himself to the Fundamental Theorem
of Algebra, taking only 22 years in his doctoral thesis. It was the first
mathematician who proved that every equation has at least one complex
root, getting acceptance by mathematicians of complex numbers, which had
been previously studied by Wallis and Euller, but referred to them as
impossible numbers, with explanations very lame for the rest of
mathematicians.

11. GAUSS FORMULAS

12. Purpose of mathematics
 The fundamental purpose of education is to develop mathematical reasoning
and abstraction, and its instrumental character.
 The mathematics are linked to the progress of civilization has been catching
and contribute to the development and formalization of Experimental and
Social Sciences
 Moreover, the mathematical language, is an effective tool that helps us better
understand the reality around us and adapt to a changing environment
everyday. Consequently, the learning of mathematics provides the opportunity
to discover the possibilities of our own understanding and strengthen our
personality, plus a cultural background necessary to handle in practical
aspects of daily life as well as to access other branches of science .

13. OBJECTIVES OF TEACHING
MATHEMATICS.
 1. Use the forms of logical thinking in various fields of human activity.
 2. Apply the mathematical tools properly acquired situations of daily life.
 3. Correctly use mathematical language in order to communicate in a clear, concise, precise and rigorous.
 4. Using critically different technological resources (calculators, computer programs) so involving an aid in learning and instrumental
applications of mathematics.
 5. Solve math problems using different strategies, procedures and resources, from intuition to the algorithms.
 6. Apply geometric knowledge to understand and analyze the physical world around us.
 7. Using statistical and probabilistic methods and procedures to draw conclusions from data collected in the information world.
 8. Integrate mathematical knowledge on the set of insights that students should acquire during their education.

14. thanks