Pascal's triangle

In mathematics, Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Persia, China, and Italy.

The rows of Pascal's triangle are conventionally enumerated starting with row 0, and the numbers in each row are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number directly above and to the left with the number directly above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

Importance of History of Science

The essence of studying the history of science is for us to know the people who contributed in the field of science and for us to find out the different changes and improvements that give progress to the science and the modern science.

PHILOSOPHY

PHILOSOPHY

-Science of theory of knowledge. -A formulated ideas base from science/ it undergoes scientific method. PHILO- LOVE SOPHIA- WISDOM

Views About Philosophy

• Aristotle-Philosophy is a thinking w/c aims at maximum connected at the truth about all available experience.


• Brittle-Is a science of being in their ultimate reasons, causes and principles acquired by the aid of numerous reasons alone.


• Smith and Tiler- It is the personal attitudes towards life and universe. -A method of reflective thinking and reasons in inquiry. -Attempt to gain a view of the whole. -Is a logical analysis of knowledge and clarification of the meaning of words and concept .

-Is a group of problems as well as theories and of this problem. The ultimate goal of the philosophy

APPROACH

Science- object of study part by part.

Philosophy- attempt to do it as a whole

Its drive

SCOPE

Science- Tends to eliminate the personal factor and ignore values in its drive objectively.

Philosophy- interested in personality, values and all realm of human experience.

NATURE

Science- aim to absorb nature and to control process.

Philosophy – criticize, evaluate and integrate various ways of life.

FUNCTIONS OF PHILOSOHY

1. To carefully examines and criticize the premises and conclusion of all sciences such as biology, physics, sociology, anatomy, (chemistry) and to compare the assumptions and conclusions of different sciences when the results appear to be contradictory.

2. To synthesize finding . (combine)

3. To harmonize and bring these and other sciences together to complement and/or support one another.

TWO MAJOR CATEGORIES OF PHILOSOPHY

Theoretical Philosophy

Directs itself to knowing things as they are without thinking of application. Its ultimate aim is knowledge of truth.

a) Metaphysics- d.) Theodicy

b) Ontology e.) Psychology

c) Cosmology f.) Epistemology

Practical Philosophy

Directs the concern to things which are material or perceptible and useful. Each goal is not just finding the truth but acting on it.

a) Semantic

b) Logic

c) Ethics

d) Axiology

e) Aesthetics

A. MAJOR FUNCTIONS OF PHILOSOPHY

a) Construct theories about man and the universe.

b) To examine very carefully everything that maybe offered for a belief and its own theories.

B. ANALYSIS

From the Greek word “analusis” which means to breakdown, is the process of breaking down topic or substance to gain or better understanding.

C. THREE MAIN WAYS OF FORMING ANALYSIS

a) Explication- which was so called by critique who work largely I the construction of symbolic language. Explicatum part by part.

b) Redefiniton - it is associated with more replacing term or statement which has the same meaning with the same sort of language but which more carefully formulated and more clearly understand.

c) Illustration- which takes the opposite point of view holding who practiced by Wittgenstein by just keeping close to multiplying use of one term to another.

KNOWLEDGE

I s defined expertise and skills acquired by a person through experience or education.

Acquisition involves complex cognitive processes.

Confident understanding of a subject with ability to use for a specific purpose.

THE FOUR MATTER OF FACTS

1. That something that ecist.

2. That something that can be known

3. That there is something which matter

4. That something includes the forgoing statements.

FOUR BRANCHES OF PHILOSOPHY

1. Ontology or the theory of being.

2. Epistemology or the theory of knowledge.

3. Axiology or the theory of value.

4. Logic or the theory of inferences.

PERCEPTION Is the process of attaining awareness or understanding of sensory information. Means “receiving, collecting, action of taking possession. Apprehension with the mind or sense

Edmund Husserl

Bracketing, This means forgetting the time being, all that one has learned, in order to take an unprejudiced look at work is presented.

Mis-judgement

“what one perceives is a result of interplays between past experiences, including one’s culture and the interpretation of the perceived.”

Thoughts, act of thinking; that which one thinks; opinions and reflections

Concept, are really habits of expectations; serves as a representation of an objects; It is idea or mental image

Percepts, views; reflections; impressions

Titchener, used to report what come into his head when he was using certain ideas. (Image Theory)

Hume, used by introspecting to discover what the self looks like, “bondless of perception”

Language Is an abstract system of word meaning and symbols of all aspects of culture. It includes speech, written character, numerals symbols, gesture and expression of non-verbal communication.

Object, the things in which the signs stands for.

Interpreter, the person who does the sign in which the sign stands for.

Sign, it represent what object is.

Term in percept as “sense meaning,” according to C.I. Lewis in simple way is study of its use and effect of the circumstances in which people employ it or react more or less consistently.

All terms have perceptual meaning, But there are some terms that do not have meaning that fall into two classes.

Grammatical term

Abstract term

All language begin on ordinary language under the process of immediate necessity of communication but not in all cases like

-customary usage as how it spread

-grammatical term

-declension case spread fall down

Ordinary Language Analysis, Is the argument that any language which is adequate stands as the transmitter of nuances or differences and shades of meaning on which everyday conversation must be fluid.

Classification

-Distinction, Identification and organization of two or more items, information and facts according to their similarities which are determined through comparison.

-Gives a closer view on the link between the object being compared.

Definition of Classification According to Gottfried Wilhelm Von Leibniz; It is the differentiation of two or more objects and that these two objects are not “ever exactly alike.” In fact, no two things are “ever exactly alike,” that if ever there were two objects which were so alike, they would be same object. There is always an “Essential Dissimilarity” even in a pair of apparently identical objects.

Plato’s Theory of Universals

Universalia in Re (Universal in the things), everything is a combination of form and form

Universalia ante rem (Universal before the things),the link between members of a class in that they are all imitati ore the thingson of an archetype which existed before the world was made.

Universalia post rem (Universal after the things), nothing general exist particular things.

Four Different Types of Similarity

Genetic Similarity, having similar origins

Structural Similarity, having the same constituent past

Functional Similarity, having similar behavior.

Apparent Similarity, having similar external features.

Maybe the statement of the essential properties of certain thing or the statement of the equivalent bet. One expression or another, usually more complex expression that gives meaning of firsts.

Definiendum, a thing being define.

Definience, the expression which defines.

Lexical definition, a dictionary definition reports the meaning of the word as if normally used.

Extensional definition, general term is just the collection of individual things to which is correctly applied.

Intentional definition, of a general term, on the other hand is the set of features which are shared by everything to which it applies.

Contextual Definition, some words cannot be clearly defined on their own , but it is impossible to offer schema for defining every sentence which they occur.

Stipulative Definition, is the specification of a meaning, adapted or assume specifically for the purposes of argument or discussion in a given context.

Ostensive Definition, gives the meaning of a term by pointing out the thing donated by,it, or pointing out by example of the kind of thing meant by it.

Precising Definition,is the definition that extends the dictionary definition of a term for specific purpose by including additional criteria that narrow down the set of things meeting the definition.

Operational Definition,of a quality is a specific process where by it is measured.

AXIOM AND THEOREM

Axiom,is a proposition that is not prove or demonstrated but considered self-evident or subject to necessary definition.

Theorem,is a statement which has been proven or has been established its validity.

HISTORICAL BACKGROUND

The early Greeks developed like LOGICO-DEDUCTIVE METHOD where by conclusion (new knowledge) follow from premises (old knowledge).

Euclid stablished common nations (very basic self-evident assertion)

Axiomatic System,any set of axioms from which some or all axioms can be used in conjunction to logically derived theorem.

Characteristics of Axiomatic System

· Independent, if it is not a theorem that can be derived from other axioms in the system.

· Complete, if for every system, either, itself or its negation is derivable,

· Consistent, if its lacks of contradiction.

ASTRONOMY

It is the study of celestial bodies or objects such as; stars, planets, comets and galaxies and its phenomena.

Greek word “ASTRON”-Stars “NOMOS”- Laws

Two major categories during the 20^th century

· Observational Astronomy- Focused on acquiring data from observation which then analyzed by the aids of basic principles of physics.

· Theoretical Astronomy- Oriented towards the development computer or analytical models to described astronomical objects and phenomena

Some Contribution of Early Civilization

Babylonian- beginning of mathematical and scientific astronomy. They discovered the lunar eclipse recorded in repeating cycle known as a “saros”.

Greek (3^rd B.C)

Aristarchus- calculated the mass of the earth and measures the distance and the size of the moon and stars. He also the 1^st to proposed a heliocentric model of the solar system.

Hipparchus-invented the 1^st and the earliest known astronomical/ device such as the “astrolabe”

= “Antikythera Mechanism (150-80 BC) wasn early analog computer designed to calculate the location of sun, moon , and earth.

Persians

Azophi- discover the Andromeda alaxy and described in his “ Book of Fixed Stars”

Egyptians- ALI IBN RIDWAN – first discovered the SN Supernova 1006, the brightest apparent magnitude stellar event recorded the history.

SOLAR SYSTEM INDIVIDUALS

1. Inner Planets- consists of Mercury, Venus, Earth, Mars.

2. Asteroids Pelts- composed of asteroids

3. Outer Planets- consists of giant gas planets such as Jupiter, Saturn, Uranus and Neptune.

STELLAR ASTRONOMY - Study of stars and its formation

EXTRA GALLACTIC ASTRONOMY- Study of objects outside the galaxy

GALMETRIC ASTRONOMY- study of galaxies.

ORGANIZATION AND DISTRIBUTION OF GALAXIES

1. Elliptical Galaxy- cross-sectional

2. Spiral Galaxy- flat-rotating disc

3. Irregular Galaxy- chaotic appearance

SCIENCE IN GREEK AND ROMAN CIVILIZATION

A. Greek Civilization – emerged around 1100 B.C. Early Greeks have been fully-developed basic elements of Mathematics, Astronomy, Physics, Geography and Medicine.

B. Persons who give contribution on the development of Science

1. Thales- matter was composed of convertible into water

2. Hippocrates- Father of Medicine

3. Aristotle- Classification of Plants and Animals

4. Pythagoras- Pythagorian Theorem

5. Archimedes- Principles of Lever and Pulley

6. Ptolemy- Geocentric Theory

C. Roman civilization- time of Julius Caesar (102-44 B.C) It is said that Romans were poor in Science but contributed a lot in the fields of infrastructure.

D. Romans that gives contributions in the field of Science

1. Pliny the Elder- only roman scientist that is celebrated. (scientific worker)

2. Galen- wrote 150 books on medicin. (physician)

3. Cleopatra- roman queen who uses cosmetics

STONE AGE TECHNOLOGY

EARLIEST COMMUNITIES

Ø Live almost entirely in small nomadic communities

Ø Surviving in his skills in hunting and fishing

Ø Develop in tropical latitudes, especially in Africa

Ø Move out thence into the subtropical regions and eventually into the land mass of Eurasia

NEOLITIC REVOLUTION

Ø Increase in population

Ø Bigger in community

Ø Beginning of town life, sometimes called as New Neolitic Revolution

Ø Primitive man used: wood, bone, fur, leaves , grasses.

STONE -materials that gives its name and technological unity

-became tools only when they were shaped deliberately for specific purposes and for this to be done efficiently.

FLINT - became a very popular stone for this purpose although fine sand stones and certain volcanic

rocks were also widely used.

v STONE- clay and bricks, animal skin, metallic oxide

FIRE - was the most important contribution of pre-historic to power technology

v TOOLS AND WEAPONS

§ Stone – headed spear

§ The harpoon

§ Bow and arrow

v OTHER DEVICES INVENTED

§ Potters wheel-driven by kicks from the operator

§ Wheels-gave continuous rotary movement in one direction

§ Drill and the lathe- derived from the bow and had the effect of spinning the drill piece

v FOOD PRODUCTION

§ Paleolitic- gathering, fishing and hunting

§ Neolitic- agriculture, and animal husbandry

v BUILDING TECHNIQUES

§ Impressive structure were created

§ Primary tombs

§ Burial, mounds and religious edifices

§ Sun-dried bricks for domestic housing

v MANUFACTURING

§ Grinding corn ( quern)- transport and communication

§ Baking clay (pottery)

§ Spinning and weaving textiles

§ Dyeing , fermenting ,and distilling

§ Gold, silver, copper, tin

§ Domestication of animals

§ Dugout canoe and brick- bark canoe

THE URBAN REVOLUTION (3000-500 B.C.)

Ø A very important cultural transition began.

Ø Generated new needs and resources and accompanied by a significant increase in a technological innovation.

Ø The beginning of the invention of the city

CATEGORIES IN THE URBAN REVOLUTION.

I. Craftsmen and Scientist-

a. led to the search for the other metallic ores, to the development and encouragement of trade in order to secure scientific metals ;

b. Rise of the first civilization

c. Summerian Astronomers

Plotted the motion of heavenly bodies

Based calculations about calendar

Relationship between science and technology have emerged

II. COPPER AND BRONZE- Goldsmith the technique of heating the metal in credible over a strong fire and casting it into simple clay or stone

BRONZE- is the most important materials of the early civilization.

III. SEA TRNSPORATION – progress from sailing ship to vessels

IV. IRRIGATION- development of systematic irrigation

V. Urban manufacturing

Centered products such as:

§ Pottery

§ Wine

§ Oil

§ Cosmetics

….these products became the commodities traded of metals

v SCIENCE OF CHEMISTRY- started in the kitchen

v WHEELED VEHICLES- primarily provided by animals ; chariot- during war it has appeared as a weapon

v BUILDING- used sun-dried bricks ; Sumerians – first to built columns with bricks; Egyptians- used stones to construct pyramids and temples.

v DISSEMINATION OF TECHNICAL KNOWLEDGE

ISLAMIC SCIENCE

Islamis culture is the most relevant to European science.

Greek -> Arabic -> Latin -> Hebrew

§ The Arabic culture and language spread afar : to Portugal, in the west and the frontiers of China in the east and over many degrees of latitude.

§ The most characteristic Arabic scientific developments were in: Alchemy, Math, Astronomy and Astrology, Medicine.

ALCHEMY

Medieval chemical art whose principal objectives were to find the panacea and to transmute based metals into gold.

RHAZES- makes the earliest known suggestions for furnishing chemical laboratory.

MATH

§ Arabic Numerals- an Indian system of numerical notation during the ninth century. It was invented in India, passed through Persia to Arabs, and was introduced in Europe in the tenth century

§ Persian Mohammad Ibn al- Khwarizmi, is the Persian Mohammad where algorism, which is medieval word for arithmetic came from. He also develop the process of rectification.

ASTRONOMY AND ASTROLOGY

Constant preoccupation of the Islamic word. It was develop in Spain. Cordova- southern Spain; Toledo – central Spain.

§ TOLEDAN- the tables of proposition of stars which were drawn up in 1080.

§ PTOLEMIC- was replaced by these concentric system

MEDICINE

§ Rhazes- made the first distinction between measles and smallpox

§ Avicenna- Persian philosopher and physician, called the Prince of Physicians

The greatest Arabic contribution to Medicine is the introduction of the new vegetable drugs.

o .

INDIAN SCIENCE

The Indian Civilization is about the oldest, still alive and it achieve a high level of technology of an early stage.

The Science and Technology in India has something to do with ff:

- Agriculture
- India Astrology
- Zinc Metallurgy
- Mathematics

List of Indian Invention and Discoveries

Atonism
- According to Democritus the term Atomos means uncuttable, or the smallest invisible particle of matter.
- Dharmakirti and Dignaga, they consider atoms to be:
1. point size
2. duration less
3. made of energy

Chandrasekhar limit and Chandrasekhar numbers.
- Discovered by the name after Subramanyan chandrasekhar, received novelty prize in physics.

Universe
- the earliest known philosophical models of the universe found in Vedas.

Indigo
- use as a dye in India

Firearms
- by the 16th century India were manufacturing a diverse variety of firearms


CHINESE SCIENCE

Silk road -an ancient trade route linking China with Rome

Important Person

Marco Pol0 - Venetian traveler and author, whose account of his travels and
experiences in China offered Europeans a first hand view of Asian land and
stimulated interests in Asian trade.

Zu Chongzhi - 15h century mathematician who calculated "pi" to the 7th digit

Liu Ju-Hsieh - mathematician who discovered Pascal's Triangle.

Tao Ch'ien - a famous poet and philosopher who influenced the idea to discover
an elixir and the science of medicine.

Four Great Inventions

Magnetic Compass
Printing Press
Gun Powder
Paper Making

Other Inventions

Astronomy
Mathematics
Military
Medicine