MATHEMATICS IN THE MODERN WORLD

HISTORY OF MATHEMATICS

• The Early Egyptians (6000 BCE)

- The Early Egyptians Settled Along the Fertile Nile Valley as Early as
About 6000 BCE And They Began to Record the Patterns of Lunar
Phases and The Seasons Both for Agricultural and Religious
Reasons.

• Oldest Mathematical Text Ancient Egypt (2000 BCE- 1800 BCE)

- The Oldest Mathematical Text From Ancient Egypt Discovered
So Far , Though , Is The Mascow Paprus , Which Dates From
The Egyptian Middle Kingdom Around 2000-1800 BCE

• Written Egyptian Numbers (2700 BCE)

- It is thought that the Egyptians introduced the earliest fully-
developed base 10 numeration system at least as early as 2700
BCE (and probably much early). Written numbers used a stroke
for units, a heel-bone symbol for tens, a coil of rope for
hundreds and a lotus plant for thousands, as well as other
hieroglyphic symbols for higher powers of ten up to a million.
MATHEMATICS IN THE MODERN WORLD
Jeffany Ann V. Lacorte

• Babylonians have multiplication Tables (1800 BC) provide evidence of the use of arithmetic operations such as
- Many of the mathematical tablets are "problem texts:" they addition, subtraction, multiplication, fractions, squares, cubes
contain problems or sets of problems, sometimes with solutions. and roots.
Many of the problems involve geometry; the rest are almost
always "word problems" where the context is the calculation of • Greek Classical Mathematics (624 BC-548 BC)
the area of an irregular field, the volume of a ditch, the number - Historians traditionally place the beginning of Greek
of bricks to build a ramp,and etc mathematics proper to the age of Thales of Miletus (ca. 624–548
BC). Little is known about the life and work of Thales, so little
indeed that his date of birth and death are estimated from the
eclipse of 585 BC, which probably occurred while he was in his
prime. Despite this, it is generally agreed that Thales is the first
of the seven wise men of Greece. The two earliest mathematical
theorems, Thales' theorem and Intercept theorem are attributed
to Thales.

• Greek Classical Mathematics (548 BCE)

- Thales is also thought to be the earliest known man in history to
whom specific mathematical discoveries have been attributed.
Although it is not known whether or not Thales was the one who
introduced into mathematics the logical structure that is so
• Early Chinese Mathematics (1600 BC) ubiquitous today, it is known that within two hundred years of
- Simple mathematics on Oracle bone script date back to the Thales the Greeks had introduced logical structure and the idea
Shang Dynasty (1600–1050 BC). One of the oldest surviving of proof into mathematics.
mathematical works is the Yi Jing, which greatly influenced
written literature during the Zhou Dynasty (1050–256 BC). For • Greek Hellenistic (547 BC)
mathematics, the book included a sophisticated use of - Most of the mathematical texts written in Greek have been
hexagrams. Leibniz pointed out, the I Ching contained elements found in Greece, Egypt, Asia Minor, Mesopotamia, and Sicily.
of binary numbers.
• Babylonian Mathematics (539 BC)
• Indian Mathematics (1000 BCE) - Babylonian mathematics (also known as Assyro-Babylonian
- Mantras from the early Vedic period (before 1000 BCE) invoke mathematics) was any mathematics developed or practiced by
powers of ten from a hundred all the way up to a trillion, and the people of Mesopotamia, from the days of the early
MATHEMATICS IN THE MODERN WORLD

Sumerians to the fall of Babylon in 539 BC. Babylonian • Chinese Mathematics (263 CE)
mathematical texts are plentiful and well edited. - Among the greatest mathematicians of ancient China was Liu
Hui, who produced a detailed commentary on the “Nine
Chapters” in 263 CE, was one of the first mathematicians known
to leave roots unevaluated, giving more exact results instead of
approximations

• Greek Hellenistic Mathematics (450 BCE)

- by the hellenistic period, theb greeks had presided over one of • European Middle Ages (301-1500)
the most dramatic and important revolutions in mathematical - When Chinese, Islamic, and Indian mathematicians had been in
thought of time . the ancient greek numeral system , known as ascendancy, and Europe fell in Dark Ages, almost all
attic or herodianic numerals, was fully developed by about 450 mathematics and intellectual endeavor stagnated.
bce , and in regular use possibly as early as the 7th century bce .From the 4th to the 12th century, studies of geometry,
arithmetic, and translations was limited to Boethius translations
of some words of ancient Greek masters.
MATHEMATICS IN THE MODERN WORLD
Jeffany Ann V. Lacorte

• India Mathematics (400-1600 CE) - The invention of the logarithm in the early 17th century was
- In the classical period of Indian mathematics (400 CE to 1600 CE), made by John Nopier. French Mathematician, Girard Desargues,
important contributions were made by scholars like Aryabhata, is considered a founder of field of protective.
Brahmagupta, Mahāvīra, Bhaskara II, Madhava of
Sangamagrama and Nilakantha Somayaji.
-The decimal number system in worldwide use today was first
recorded in Indian mathematics

• Islamic Middle Ages (632-1258)

- The Islamic Empire made significant contributions to math, since
the 8th century.Over time, Muslim artists discovered all different
types of symmetry that can be done on a 2D surface.

• Renaissance 18th century (1701-1800)

- France became more prominent towards the end of the century.
.Joseph Louis Largrange worked with Euler in a join work on the
calculus of variation.

• 19th century math (1801-1900)

- Jean-Robert Argand posted a paper on how complex numbers
can be shown on geometric diagrams. George Peacock is usual
credited with the invention of symbolic algebra.

• Modern Abstract Math (1801-1900)

• th
Renaissance 16 century (1501-1600) - Abstract math is a branch of math concerned with the general
- An important person in the early 16th century was an Italian algebraic structure of various sets. A definitive treatise, Modern
Franciscan friar named Luca Pacioli. Later, multiplication, Algebra, was written by Bartel van der Waerden, and it impacted
division, decimal, and inequality symbols were getting more all branches of math,
recognized.

• Renaissance 17th Century (1601-1700)

MATHEMATICS IN THE MODERN WORLD
Jeffany Ann V. Lacorte

• 20th Century Math (1901-2000) - Phi is an irrational number with a value of approximately
- In the early 20th Century, there was the beginnings of the rise of 1.618033988 which expresses the relationship that the sum of
the field of mathematical logic. Hilbert was responsible for two quantities is to the larger quantity as the larger is to the
several theorems and some entirely new mathematical concepts. smaller.

• 21st Century math (2001-present) FIBONNACI SEQUENCE

- Here in the present, we learn from our history to then discover
new branches of math. Our math will evolve more in time, as in - The next number is found by adding up the two numbers before
more formulas and answers. it:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393,
FUNCTIONALITY OF MATHEMATICS 186418, ….

- Mathematics is relevant. Mathematics is a body of knowledge. TRANSFORMATION

Therefore, it is only given that it has applications not just in the
field of mathematics but also in other fields. - Changes the size, shape, or position of a figure and creates a new
figure.
- A geometry transformation is either rigid or non-rigid; another
word for a rigid transformation is “isometry”.
PATTERNS
- A general term for four specific ways to manipulate the shape
and/or position of a point, line, or geometric figure.
- There are two types of patterns: numeric and geometric. - Original shape of the object is called the pre-image and the final
Numeric patters are also known as number patterns. Geometric shape and position of the object is the image under the
patterns are visually represented by shapes. transformation.

ISOMETRIES
GOLDEN RATIO
- One-to-one transformation from one geometric space onto itself
- The golden ratio is denoted by (phi). This special ratio is also which preserves all intrinsic properties such as length, angle
called the divine proportion. This is because the human beauty is measure, and area.
based on the divine proportion.
MATHEMATICS IN THE MODERN WORLD
Jeffany Ann V. Lacorte

• FRIEZE PATTERNS
FOUR TYPES OF TRANSFORMATION IN
- One-directional; reflection; translation, and glide reflection along
MATHEMATICS one line

• TRANSLATION • WALLPAPER PATTERNS

- Simply means moving - Two-directional; rotation, reflection, and glide reflection;
- The size of the image is the same size as the pre-image translation in two linearly independent directions
- Those that repeat in more than one direction
• ROTATION
- Means turning around a center 2 TYPES OF SYMMETRY
- The pre-image and image are the same
• CYCLIC SYMMETRY: rotation symmetry around a center but no
• REFLECTION mirror lines.
- Means mirroring or flipping
- The length is equidistant • DIHEDRAL SYMMETRY: rotation symmetry around a center point
with mirror lines through the center point.
• DILATION
- It means resizing
- The size is changing
MATHEMATICAL LANGUAGE AND
SYMBOLS
SYMMETRY
- CHARACTERISTICS OF MATHEMATICAL LANGUAGE
- An object or shape is symmetrical when it remains unchanged • Powerful which means able to express complex thoughts with
after we rotate, flip or scale it and when it allows being divided relative ease
into parts of equal shape and size. • Nontemporal for it does not follow tenses
- Well-proportioned, well-balanced • Has its own vocabulary and parts of speech

GEOMETRIC DESIGNS

• ROSETTE PATTERNS
- Finite design; reflection and rotation those that repeat in no
direction