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Vector Difference

Well Isn`t  2-1 Same As 2 + (-1)
In The Same Way In Vectors We Add The Negative Of A Vector To Find Difference Between Two Vectors.

Vectors Like Scalars Cant Be Added Using Normal Mathematical Rules Of Addiation 

Triangle Law Of Vector Addiation

Parallelogram Law Of Vector Addiation

Scalars Vs Vectors

In science and engineering we frequently encounter quantities that have magnitude and
magnitude only: mass, time, and temperature. These we label scalar quantities, which remain
the same no matter what coordinates we use. In contrast, many interesting physical
quantities have magnitude and, in addition, an associated direction. This second group
includes displacement, velocity, acceleration, force, momentum, and angular momentum.
Quantities with magnitude and direction are labeled vector quantities. Usually, in elementary
treatments, a vector is defined as a quantity having magnitude and direction. To distinguish
vectors from scalars, we identify vector quantities with boldface type, that is, V.
Our vector may be conveniently represented by an arrow, with length proportional to the
magnitude. The direction of the arrow gives the direction of the vector, the positive sense
of direction being indicated by the point.

Emergence of experimental method and physical optics

The use of empirical experiments in geometrical optics dates back to second century Roman Egypt, where Ptolemy carried out several experiments on reflection, refraction and binocular vision. However, he either discarded or rationalized any empirical data that did not support his Platonic paradigm. Experiments did not hold any importance at the time, and empirical evidence was thus seen as secondary to general theory. The incorrect emission theory of vision thus continued to dominate optics through to the 10th century.

The turn of the second millennium saw the development of an experimental method emphasizing the role of experimentation as a form of proof for scientific inquiry together with the development of physical optics where mathematics and geometry were combined with the philosophical field of physics. The Iraqi physicist, Ibn al-Haytham (Alhazen), is considered a central figure in this shift in physics from a philosophical activity to an experimental and mathematical one, and the shift in optics from a mathematical discipline to a physical and experimental one.

Due to his positivist approach, his Doubts Concerning Ptolemy insisted on scientific demonstration and criticized Ptolemy's confirmation bias and conjectural undemonstrated theories. His Book of Optics (1021) was the earliest successful attempt at unifying a mathematical discipline (geometrical optics) with the philosophical field of physics, to create the modern science of physical optics. An important part of this was the intromission theory of vision, which in order to prove, he developed an experimental method to test his hypothesis. He conducted various experiments to prove his intromission theory and other hypotheses on light and vision. The Book of Optics established experimentation as the norm of proof in optics, and gave optics a physico-mathematical conception at a much earlier date than the other mathematical disciplines. His On the Light of the Moon also attempted to combine mathematical astronomy with physics, a field now known as astrophysics, to formulate several astronomical hypotheses which he proved through experimentation.

Back To Past :History Of Physics

Elements of what became physics were drawn primarily from the fields of astronomy, optics, and mechanics, which were methodologically united through the study of geometry. These mathematical disciplines began in Antiquity with the Babylonians and with Hellenistic writers such as Archimedes and Ptolemy. Meanwhile, philosophy, including what was called “physics”, focused on explanatory (rather than descriptive) schemes, largely developed around the Aristotelian idea of the four types of “causes”.

The move towards a rational understanding of nature began at least since the Archaic Period in Greece (650 BCE – 480 BCE) with the Pre-Socratic philosophers. The philosopher Thales (7th and 6 centuries BCE), dubbed "the Father of Science" for refusing to accept various supernatural, religious or mythological explanations for natural phenomena, proclaimed that every event had a natural cause.Leucippus (first half of 5th century BCE), developed the theory of atomism — the idea that everything is composed entirely of various imperishable, indivisible elements called atoms. This was elaborated in great detail by Democritus.

Aristotle (Greek: Ἀριστοτέλης, Aristotélēs) (384 BCE – 322 BCE), a student of Plato, promoted the concept that observation of physical phenomena could ultimately lead to the discovery of the natural laws governing them. He wrote the first work which refers to that line of study as "Physics" (Aristotle's Physics). During the classical period in Greece (6th, 5th and 4th centuries BCE) and in Hellenistic times, natural philosophy slowly developed into an exciting and contentious field of study.

Early in Classical Greece, that the earth is a sphere ("round"), was generally known by all, and around 240 BCE, Eratosthenes (276 BCE - 194 BCE) accurately estimated its circumference. In contrast to Aristotle's geocentric views, Aristarchus of Samos (Greek: Ἀρίσταρχος; 310 BCE – ca. 230 BCE) presented an explicit argument for a heliocentric model of the solar system, placing the Sun, not the Earth, at the centre. Seleucus of Seleucia, a follower of the heliocentric theory of Aristarchus, stated that the Earth rotated around its own axis, which in turn revolved around the Sun. Though the arguments he used were lost, Plutarch stated that Seleucus was the first to prove the heliocentric system through reasoning.

In the 3rd century BCE, the Greek mathematician Archimedes laid the foundations of hydrostatics, statics and the explanation of the principle of the lever. In his work On Floating Bodies, around 250 BCE, Archimedes develops the law of buoyancy, also known as Archimedes' Principle. The astronomer Ptolemy wrote the Almagest, a comprehensive astronomical text that formed the basis of much later science.

Much of the accumulated knowledge of the ancient world was lost. Even of the works of the better known thinkers, few fragments survived. Although he wrote at least fourteen books, almost nothing of Hipparchus' direct work survived. Of the 150 reputed Aristotelian works, only 30 exist, and some of those are "little more than lecture notes". Though reinterpreted to fit theological concerns, both Jewish and Islamic scholarship preserved and developed some of the ancient knowledge that would otherwise have been lost.

The Islamic Abbasid caliphs gathered many classic works of antiquity and had them translated into Arabic. Islamic philosophers such as Al-Kindi (Alkindus), Al-Farabi (Alpharabius), Avicenna (Ibn Sina) and Averroes (Ibn Rushd) reinterpreted Greek though in the context of their religion. Important contributions were made by Ibn al-Haytham and Abū Rayhān Bīrūnī before eventually passing on to Western Europe where they were studied by scholars such as Roger Bacon and Witelo.

Awareness of ancient works re-entered the West through translations from Arabic to Latin. Their re-introduction, combined with Judeo-Islamic theological commentaries, had a great influence on Medieval philosophers such as Thomas Aquinas. Scholastic European scholars, who sought to reconcile the philosophy of the ancient classical philosophers with Judeo-Christian theology, proclaimed Aristotle the greatest thinker of the ancient world. In cases where they didn't directly contradict the Bible, Aristotelian physics became the foundation for the physical explanations of the European Churches.

Based on Aristotelian physics, Scholastic physics described things as moving according to their essential nature. Celestial objects were described as moving in circles, because perfect circular motion was considered an innate property of objects that existed in the uncorrupted realm of the celestial spheres. The theory of impetus, the ancestor to the concepts of inertia and momentum, was developed along similar lines by medieval philosophers such as John Philoponus, Avicenna and Jean Buridan. Motions below the lunar sphere were seen as imperfect, and thus could not be expected to exhibit consistent motion. More idealized motion in the “sublunary” realm could only be achieved through artifice, and prior to the 17th century, many did not view artificial experiments as a valid means of learning about the natural world. Physical explanations in the sublunary realm revolved around tendencies. Stones contained the element earth, and earthy objects tended to move in a straight line toward the centre of the earth (and the universe in the Aristotelian geocentric view) unless otherwise prevented from doing so.


Important physical and mathematical traditions also existed in ancient Chinese and Indian sciences. In Indian philosophy, Kanada of the Vaisheshika school proposed the theory of atomism during the 1st millennium BCE,and it was further elaborated on by the Buddhist atomists Dharmakirti and Dignāga during the 1st millennium CE.In Indian astronomy, Aryabhata's Aryabhatiya (499 CE) proposed the Earth's rotation, while Nilakantha Somayaji (1444–1544) of the Kerala school of astronomy and mathematics proposed a semi-heliocentric model resembling the Tychonic system. In Chinese philosophy, Mozi (c. 470-390 BCE) proposed a concept similar to inertia, while in optics, Shen Kuo (1031–1095 CE) independently developed a camera obscura. The study of magnetism in China dates back to the 4th century BCE (in the Book of the Devil Valley Master),eventually leading to the invention of the compass.

The Main Part :Math (Relation To Math)

Relation to mathematics and the other sciences

In the Assayer (1622), Galileo noted that mathematics is the language in which Nature expresses its laws.Most experimental results in physics are numerical measurements, and theories in physics use mathematics to give numerical results to match these measurements.

Physics relies upon mathematics to provide the logical framework in which physical laws may be precisely formulated and predictions quantified. Whenever analytic solutions of equations are not feasible, numerical analysis and simulations may be utilized. Thus, scientific computation is an integral part of physics, and the field of computational physics is an active area of research.

A key difference between physics and mathematics is that since physics is ultimately concerned with descriptions of the material world, it tests its theories by comparing the predictions of its theories with data procured from observations and experimentation, whereas mathematics is concerned with abstract patterns, not limited by those observed in the real world. The distinction, however, is not always clear-cut. There is a large area of research intermediate between physics and mathematics, known as mathematical physics.

Physics is also intimately related to many other sciences, as well as applied fields like engineering and medicine. The principles of physics find applications throughout the other natural sciences as some phenomena studied in physics, such as the conservation of energy, are common to all material systems. Other phenomena, such as superconductivity, stem from these laws, but are not laws themselves because they only appear in some systems.

Physics is often said to be the "fundamental science" (chemistry is sometimes included), because each of the other disciplines (biology, chemistry, geology, material science, engineering, medicine etc.) deals with particular types of material systems that obey the laws of physics.[8] For example, chemistry is the science of collections of matter (such as gases and liquids formed of atoms and molecules) and the processes known as chemical reactions that result in the change of chemical substances.

The structure, reactivity, and properties of a chemical compound are determined by the properties of the underlying molecules, which may be well-described by areas of physics such as quantum mechanics, or quantum chemistry, thermodynamics, and electromagnetism.