1.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
2.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
3.
Electromagnetism
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as fields, magnetic fields. The other three fundamental interactions are the interaction, the weak interaction, and gravitation. The word electromagnetism is a form of two Greek terms, ἤλεκτρον, ēlektron, amber, and μαγνῆτις λίθος magnētis lithos, which means magnesian stone. The electromagnetic force plays a role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the force to atomic nuclei, and their orbital shapes. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, there are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential, although electromagnetism is considered one of the four fundamental forces, at high energy the weak force and electromagnetic force are unified as a single electroweak force. In the history of the universe, during the epoch the unified force broke into the two separate forces as the universe cooled. Originally, electricity and magnetism were considered to be two separate forces, Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs, every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a field, or a magnet is moved towards or away from it. While preparing for a lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from north when the electric current from the battery he was using was switched on. At the time of discovery, Ørsted did not suggest any explanation of the phenomenon. However, three later he began more intensive investigations
4.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
5.
Big Bang
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The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. If the known laws of physics are extrapolated to the highest density regime, detailed measurements of the expansion rate of the universe place this moment at approximately 13.8 billion years ago, which is thus considered the age of the universe. After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, giant clouds of these primordial elements later coalesced through gravity in halos of dark matter, eventually forming the stars and galaxies visible today. Since Georges Lemaître first noted in 1927 that a universe could be traced back in time to an originating single point. More recently, measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, the known physical laws of nature can be used to calculate the characteristics of the universe in detail back in time to an initial state of extreme density and temperature. American astronomer Edwin Hubble observed that the distances to faraway galaxies were strongly correlated with their redshifts, assuming the Copernican principle, the only remaining interpretation is that all observable regions of the universe are receding from all others. Since we know that the distance between galaxies increases today, it must mean that in the past galaxies were closer together, the continuous expansion of the universe implies that the universe was denser and hotter in the past. Large particle accelerators can replicate the conditions that prevailed after the early moments of the universe, resulting in confirmation, however, these accelerators can only probe so far into high energy regimes. Consequently, the state of the universe in the earliest instants of the Big Bang expansion is still poorly understood, the first subatomic particles to be formed included protons, neutrons, and electrons. Though simple atomic nuclei formed within the first three minutes after the Big Bang, thousands of years passed before the first electrically neutral atoms formed, the majority of atoms produced by the Big Bang were hydrogen, along with helium and traces of lithium. Giant clouds of primordial elements later coalesced through gravity to form stars and galaxies. The framework for the Big Bang model relies on Albert Einsteins theory of relativity and on simplifying assumptions such as homogeneity. The governing equations were formulated by Alexander Friedmann, and similar solutions were worked on by Willem de Sitter, extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This singularity indicates that general relativity is not a description of the laws of physics in this regime. How closely models based on general relativity alone can be used to extrapolate toward the singularity is debated—certainly no closer than the end of the Planck epoch. This primordial singularity is itself called the Big Bang, but the term can also refer to a more generic early hot. The agreement of independent measurements of this age supports the model that describes in detail the characteristics of the universe. The earliest phases of the Big Bang are subject to much speculation, in the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures and was very rapidly expanding and cooling
6.
Volcano
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A volcano is a rupture in the crust of a planetary-mass object, such as Earth, that allows hot lava, volcanic ash, and gases to escape from a magma chamber below the surface. Earths volcanoes occur because its crust is broken into 17 major, therefore, on Earth, volcanoes are generally found where tectonic plates are diverging or converging. This type of volcanism falls under the umbrella of plate hypothesis volcanism, Volcanism away from plate boundaries has also been explained as mantle plumes. These so-called hotspots, for example Hawaii, are postulated to arise from upwelling diapirs with magma from the boundary,3,000 km deep in the Earth. Volcanoes are usually not created where two plates slide past one another. Erupting volcanoes can pose hazards, not only in the immediate vicinity of the eruption. Historically, so-called volcanic winters have caused catastrophic famines, the word volcano is derived from the name of Vulcano, a volcanic island in the Aeolian Islands of Italy whose name in turn comes from Vulcan, the god of fire in Roman mythology. The study of volcanoes is called volcanology, sometimes spelled vulcanology, at the mid-oceanic ridges, two tectonic plates diverge from one another as new oceanic crust is formed by the cooling and solidifying of hot molten rock. Most divergent plate boundaries are at the bottom of the oceans, therefore, most volcanic activity is submarine, black smokers are evidence of this kind of volcanic activity. Where the mid-oceanic ridge is above sea-level, volcanic islands are formed, for example, subduction zones are places where two plates, usually an oceanic plate and a continental plate, collide. In this case, the plate subducts, or submerges under the continental plate forming a deep ocean trench just offshore. In a process called flux melting, water released from the subducting plate lowers the temperature of the overlying mantle wedge. This magma tends to be very viscous due to its high content, so it often does not reach the surface. When it does reach the surface, a volcano is formed, typical examples of this kind of volcano are Mount Etna and the volcanoes in the Pacific Ring of Fire. Because tectonic plates move across them, each volcano becomes dormant and is eventually re-formed as the plate advances over the postulated plume and this theory is currently under criticism, however. The most common perception of a volcano is of a mountain, spewing lava and poisonous gases from a crater at its summit, however. The features of volcanoes are more complicated and their structure. Some volcanoes have rugged peaks formed by lava domes rather than a summit crater while others have features such as massive plateaus
7.
Polarizing filter (photography)
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A polarizing / polarising filter is often placed in front of the camera lens in photography in order to darken skies, manage reflections, or suppress glare from the surface of lakes or the sea. Since reflections tend to be at least partially linearly-polarized, a linear polarizer can be used to change the balance of the light in the photograph, the rotational orientation of the filter is adjusted for the preferred artistic effect. This additional step avoids problems with auto-focus and light-metering sensors within some cameras, light reflected from a non-metallic surface becomes polarized, this effect is maximum at Brewsters angle, about 56° from the vertical for common glass. A polarizer rotated to pass only light polarized in the perpendicular to the reflected light will absorb much of it. This absorption allows glare reflected from, for example, a body of water or a road to be reduced, reflections from shiny surfaces are also reduced. This allows the color and detail of what is beneath to come through. Reflections from a window into a dark interior can be much reduced, some of the light coming from the sky is polarized. The electrons in the air molecules cause a scattering of sunlight in all directions and this explains why the sky is not dark during the day. But when looked at from the sides, the light emitted from an electron is totally polarized. Hence, a picture taken in a direction at 90 degrees from the sun can take advantage of this polarization, actually, the effect is visible in a band of 15° to 30° measured from the optimal direction. Perpendicularly incident light waves tend to reduce clarity and saturation of certain colors, the polarizing lens effectively absorbs these light waves, rendering outdoor scenes crisper with deeper color tones in subject matter such as blue skies, bodies of water and foliage. Much light is differentiated by polarization, e. g. light passing through crystals like sunstones or water droplets producing rainbows, the polarization of the rainbow is caused by the internal reflection. The rays strike the surface of the drop close to the Brewster angle. Polarizing filters can be rotated to maximise or minimise admission of polarised light and they are mounted in a rotating collar for this purpose, one need not screw or unscrew the filter to adjust the effect. Rotating the polarizing filter will make rainbows, reflections, and other polarized light stand out or nearly disappear depending on how much of the light is polarized, the benefits of polarizing filters are the same in digital or film photography. There are two types of polarizing filters readily available, linear and circular, which have exactly the same effect photographically, linearly-polarized light may also defeat the action of the Anti-aliasing filter on the imaging sensor. Circular polarizing photographic filters consist of a linear polarizer on the front, the quarter-wave plate converts the selected polarization to circularly polarized light inside the camera. This works with all types of cameras, because mirrors and beam-splitters split circularly polarized light the way they split unpolarized light
8.
Petrographic microscope
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A petrographic microscope is a type of optical microscope used in petrology and optical mineralogy to identify rocks and minerals in thin sections. The microscope is used in mineralogy and petrography, a branch of petrology which focuses on detailed descriptions of rocks. The method is called polarized light microscopy and these special parts add to the cost and complexity of the microscope. These might be sufficient for many non-quantitative purposes, the two Nicol prisms of the petrographic microscope have their polarizing planes oriented perpendicular to one another. Using one polarizer makes it possible to view the slide in plane polarized light, to observe the interference figure, true petrographic microscopes usually include an accessory called a Bertrand lens, which focuses and enlarges the figure. It is also possible to remove an eyepiece lens to make an observation of the objective lens surface. Nikon, Introduction to Polarized Light Microscopy Olympus, Polarized Light Microscopy Geological Microscopes A virtual Polarizing Microscope
9.
Geology
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Geology is an earth science concerned with the solid Earth, the rocks of which it is composed, and the processes by which they change over time. Geology can also refer generally to the study of the features of any terrestrial planet. Geology gives insight into the history of the Earth by providing the evidence for plate tectonics, the evolutionary history of life. Geology also plays a role in engineering and is a major academic discipline. The majority of data comes from research on solid Earth materials. These typically fall into one of two categories, rock and unconsolidated material, the majority of research in geology is associated with the study of rock, as rock provides the primary record of the majority of the geologic history of the Earth. There are three types of rock, igneous, sedimentary, and metamorphic. The rock cycle is an important concept in geology which illustrates the relationships between three types of rock, and magma. When a rock crystallizes from melt, it is an igneous rock, the sedimentary rock can then be subsequently turned into a metamorphic rock due to heat and pressure and is then weathered, eroded, deposited, and lithified, ultimately becoming a sedimentary rock. Sedimentary rock may also be re-eroded and redeposited, and metamorphic rock may also undergo additional metamorphism, all three types of rocks may be re-melted, when this happens, a new magma is formed, from which an igneous rock may once again crystallize. Geologists also study unlithified material which typically comes from more recent deposits and these materials are superficial deposits which lie above the bedrock. Because of this, the study of material is often known as Quaternary geology. This includes the study of sediment and soils, including studies in geomorphology, sedimentology and this theory is supported by several types of observations, including seafloor spreading, and the global distribution of mountain terrain and seismicity. This coupling between rigid plates moving on the surface of the Earth and the mantle is called plate tectonics. The development of plate tectonics provided a basis for many observations of the solid Earth. Long linear regions of geologic features could be explained as plate boundaries, mid-ocean ridges, high regions on the seafloor where hydrothermal vents and volcanoes exist, were explained as divergent boundaries, where two plates move apart. Arcs of volcanoes and earthquakes were explained as convergent boundaries, where one plate subducts under another, transform boundaries, such as the San Andreas Fault system, resulted in widespread powerful earthquakes. Plate tectonics also provided a mechanism for Alfred Wegeners theory of continental drift and they also provided a driving force for crustal deformation, and a new setting for the observations of structural geology
10.
Wood
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Wood is a porous and fibrous structural tissue found in the stems and roots of trees, and other woody plants. It is a material, a natural composite of cellulose fibers which are strong in tension embedded in a matrix of lignin which resists compression. Wood is sometimes defined as only the secondary xylem in the stems of trees, in a living tree it performs a support function, enabling woody plants to grow large or to stand up by themselves. It also conveys water and nutrients between the leaves, other growing tissues, and the roots, Wood may also refer to other plant materials with comparable properties, and to material engineered from wood, or wood chips or fiber. In 2005, the stock of forests worldwide was about 434 billion cubic meters. As an abundant, carbon-neutral renewable resource, woody materials have been of intense interest as a source of renewable energy, in 1991 approximately 3.5 billion cubic meters of wood were harvested. Dominant uses were for furniture and building construction, a 2011 discovery in the Canadian province of New Brunswick discovered the earliest known plants to have grown wood, approximately 395 to 400 million years ago. Wood can be dated by carbon dating and in species by dendrochronology to make inferences about when a wooden object was created. People have used wood for millennia for many purposes, primarily as a fuel or as a material for making houses, tools, weapons, furniture, packaging, artworks. Constructions using wood date back ten thousand years, buildings like the European Neolithic long house were made primarily of wood. Recent use of wood has changed by the addition of steel. The year-to-year variation in tree-ring widths and isotopic abundances gives clues to the climate at that time. This process is known as growth, it is the result of cell division in the vascular cambium, a lateral meristem. These cells then go on to form thickened secondary cell walls, composed mainly of cellulose, hemicellulose, if the distinctiveness between seasons is annual, these growth rings are referred to as annual rings. Where there is little seasonal difference growth rings are likely to be indistinct or absent, if the bark of the tree has been removed in a particular area, the rings will likely be deformed as the plant overgrows the scar. It is usually lighter in color than that near the portion of the ring. The outer portion formed later in the season is known as the latewood or summerwood. However, there are differences, depending on the kind of wood
