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An Abrahamic religion is a religion whose followers believe in the prophet Abraham. They believe Abraham and his sons/grandsons hold an important role in human spiritual development. The best known Abrahamic religions are Judaism, Christianity and Islam. Smaller religious traditions sometimes included as Abrahamic religions are Samaritanism, Druze, Rastafari, Yazidi, Babism and Bahá'í Faith. Mandaeism (a religion that holds many Abrahamic beliefs) is not called Abrahamic because its followers think Abraham was a false prophet

True Abrahamic religions are monotheistic (the belief that there is only one God). They also all believe that people should pray to God and worship God often. Among monotheistic religions, the Abrahamic religions have the world's largest number of followers. They are also all ethical monotheistic religions. This means they have rules that they have to follow.

Algebra

Algebra (from Arabic: الجبر‎, transliterated "al-jabr", meaning "reunion of broken parts") is a part of mathematics (often called math in the United States and maths or numeracy in the United Kingdom ). It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation. A very simple equation using a variable is: 2 + 3 = x. In this example, x = 5, or it could also be said that "codice_1 equals five". This is called "solving for codice_1".

Besides equations, there are inequalities ("less than" and "greater than"). A special type of equation is called the function. This is often used in making graphs because it always turns one input into one output.

Algebra can be used to solve real problems because the rules of algebra work in real life and numbers can be used to represent the values of real things. Physics, engineering and computer programming are areas that use algebra all the time. It is also useful to know in surveying, construction and business, especially accounting.

People who do algebra use the rules of numbers and mathematic operations used on numbers. The simplest are adding, subtracting, multiplying, and dividing. More advanced operations involve exponents, starting with squares and square roots.

Algebra was first used to solve equations and inequalities. Two examples are linear equations (the equation of a straight line, y=mx+b or codice_3) and quadratic equations, which has variables that are squared (multiplied by itself, for example: 2*2, 3*3, or x*x).

Early forms of algebra were developed by the Babylonians and the Greek geometers such as Hero of Alexandria. However the word "algebra" is a Latin form of the Arabic word "Al-Jabr" ("casting") and comes from a mathematics book "Al-Maqala fi Hisab-al Jabr wa-al-Muqabilah", ("Essay on the Computation of Casting and Equation") written in the 9th century by a Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, who was a Muslim born in Khwarizm in Uzbekistan. He flourished under Al-Ma'moun in Baghdad, Iraq through 813-833 AD, and died around 840 AD. The book was brought into Europe and translated into Latin in the 12th century. The book was then given the name 'Algebra'. (The ending of the mathematician's name, al-Khwarizmi, was changed into a word easier to say in Latin, and became the English word "algorithm").

Here is a simple example of an algebra problem:

These are the steps you can use to solve the problem:

With practice, algebra can be used when faced with a problem that is too hard to solve any other way. Problems such as building a freeway, designing a cell phone, or finding the cure for a disease all require algebra.

As in most parts of mathematics, adding "z" to "y" (or "y" plus "z") is written as "y" + "z".

Subtracting "z" from "y" (or "y" minus "z") is written as "y" − "z".

Dividing "y" by "z" (or "y" over "z": formula_1) is written as "y" ÷ "z" or y/z. "y"/"z" is more commonly used.

In algebra, multiplying "y" by "z" (or "y" times "z") can be written in 4 ways: "y × z", "y * z", "y·z", or just "yz". The multiplication symbol "×" is usually not used, because it looks too much like the letter x, which is often used as a variable. Also, when multiplying a larger expression, parentheses can be used: "y" ("z+1").

When we multiply a number and a letter in algebra, we write the number in front of the letter: 5 × "y" = 5"y". When the number is 1, then the 1 is not written because 1 times any number is that number (1 × "y" = "y") and so it is not needed.

As a side note, you do not have to use the letters "x" or "y" in algebra. Variables are just symbols that mean some unknown number or value, so you can use any variable. "x" and "y" are the most common, though.

An important part of algebra is the study of functions, since functions often appear in equations that we are trying to solve. A function is like a machine you can put a number (or numbers) into and get a certain number (or numbers) out. When using functions, graphs can be powerful tools in helping us to study the solutions to equations.

A graph is a picture that shows all the values of the variables that make the equation or inequality true. Usually this is easy to make when there are only one or two variables. The graph is often a line, and if the line does not bend or go straight up-and-down it can be described by the basic formula y = mx + b. The variable "b" is the y-intercept of the graph (where the line crosses the vertical axis) and "m" is the slope or steepness of the line. This formula applies to the coordinates of a graph, where each point on the line is written (x, y).

In some math problems like the equation for a line, there can be more than one variable ("x" and "y" in this case). To find points on the line, one variable is changed. The variable that is changed is called the "independent" variable. Then the math is done to make a number. The number that is made is called the "dependent" variable. Most of the time the independent variable is written as "x" and the dependent variable is written as "y", for example, in y = 3x + 1. This is often put on a graph, using an "x" axis (going left and right) and a "y" axis (going up and down). It can also be written in function form: f(x) = 3x + 1. So in this example, we could put in 5 for "x" and get y = 16. Put in 2 for "x" would get y=7. And 0 for "x" would get y=1. So there would be a line going thru the points (5,16), (2,7), and (0,1) as seen in the graph to the right.

If x has a power of 1, it is a straight line. If it is squared or some other power, it will be curved. If it uses an inequality ("<" or ">"), then usually part of the graph is shaded, either above or below the line.

In algebra, there are a few rules that can be used for further understanding of equations. These are called the rules of algebra. While these rules may seem senseless or obvious, it is wise to understand that these properties do not hold throughout all branches of mathematics. Therefore, it will be useful to know how these axiomatic rules are declared, before taking them for granted. Before going on to the rules, reflect on two definitions that will be given.

'Commutative' means that a function has the same result if the numbers are swapped around. In other words, the order of the terms in an equation do not matter. When the operator of two terms is an addition, the 'commutative property of addition' is applicable. In algebraic terms, this gives formula_6.

Note that this does not apply for subtraction! (i.e. formula_7)

When the operator of two terms is an multiplication, the 'commutative property of multiplication' is applicable. In algebraic terms, this gives formula_8.

Note that this does not apply for division! (i.e. formula_9, when formula_10)

'Associative' refers to the grouping of numbers. The associative property of addition implies that, when adding three or more terms, it doesn't matter how these terms are grouped. Algebraically, this gives formula_11. Note that this does not hold for subtraction, e.g. formula_12 (see the distributive property).

The associative property of multiplication implies that, when multiplying three or more terms, it doesn't matter how these terms are grouped. Algebraically, this gives formula_13. Note that this does not hold for division, e.g. formula_14.

The distributive property states that the multiplication of a number by another term can be distributed. For instance: formula_15. (Do "not "confuse this with the associative properties! For instance, formula_16.)

'Identity' refers to the property of a number that it is equal to itself. In other words, there exists an operation of two numbers so that it equals the variable of the sum. The additive identity property states that the sum of any number and 0 is that number: formula_17. This also holds for subtraction: formula_18.

The multiplicative identity property states that the product of any number and 1 is that number: formula_19. This also holds for division: formula_20.

The additive inverse property is somewhat like the opposite of the additive identity property. When an operation is the sum of a number and its opposite, and it equals 0, that operation is a valid algebraic operation. Algebraically, it states the following: formula_21. Additive inverse of 1 is (-1).

The multiplicative inverse property entails that when an operation is the product of a number and its reciprocal, and it equals 1, that operation is a valid algebraic operation. Algebraically, it states the following: formula_22. Multiplicative inverse of 2 is 1/2.

In addition to "elementary algebra", or basic algebra, there are advanced forms of algebra, taught in colleges and universities, such as abstract algebra, linear algebra, and universal algebra.

This includes how to use a matrix to solve many linear equations at once. "Abstract algebra" is the study of things that are found in equations, going beyond numbers to the more abstract with groups of numbers.

Many math problems are about physics and engineering. In many of these physics problems time is a variable. Time uses the letter "t". Using the basic ideas in algebra can help reduce a math problem to its simplest form making it easier to solve difficult problems. Energy is "e", force is "f", mass is "m", acceleration is "a" and speed of light is sometimes "c". This is used in some famous equations, like f = ma and e=mc^2 (although more complex math beyond algebra was needed to come up with that last equation).

Atom

Atoms are very small pieces of matter. There are many different types of atoms, each with its own name, mass and size. These different types of atoms are called chemical elements. The chemical elements are organized on the periodic table. Examples of elements are hydrogen and gold.

Atoms are very small, but their exact size depends on the element. Atoms range from 0.1 to 0.5 nanometers in width. One nanometer is about 100,000 times smaller than the width of a human hair. This makes atoms impossible to see without special tools. Scientists discover how they work and interact with other atoms through experiments.

Atoms can join together to make molecules: for example, two hydrogen atoms and one oxygen atom combine to make a water molecule. When atoms join together it is called a chemical reaction.

Atoms are made up of three kinds of smaller particles, called protons, neutrons and electrons. The protons and neutrons are heavier, and stay in the middle of the atom, which is called the nucleus. The nucleus is surrounded by a cloud of light-weight electrons, these are attracted to the protons in the nucleus by the electromagnetic force because they have opposite electric charges.

The number of protons an atom has defines what chemical element it is, this number is sometimes called its atomic number. For example, hydrogen has one proton and sulfur has 16 protons. Because the mass of neutrons and protons is very similar, and the mass of electrons is very small, we can call the amount of protons and neutrons in an atom its atomic mass.

Atoms move faster when they are in their gas form (because they are free to move) than they do in liquid form and solid matter. In solid materials, the atoms are tightly packed next to each other so they vibrate, but are not able to move (there is no room) as atoms in liquids do.

The word "atom" comes from the Greek (ἀτόμος) "atomos", "indivisible", from (ἀ)-, "not," and τόμος, "a cut." The first historical mention of the word atom came from works by the Greek philosopher Democritus, around 400 BC. Atomic theory stayed as a mostly philosophical subject, with not much actual scientific investigation or study, until the development of chemistry in the 1650s.

In 1777 French chemist Antoine Lavoisier defined the term "element" for the first time. He said that an element was any basic substance that could not be broken down into other substances by the methods of chemistry. Any substance that could be broken down was a "compound".

In 1803, English philosopher John Dalton suggested that elements were tiny, solid balls made of atoms. Dalton believed that all atoms of the same element have the same mass. He said that compounds are formed when atoms of more than one element combine. According to Dalton, in a certain compound, the atoms of the compound's elements always combine the same way.

In 1827, British scientist Robert Brown looked at pollen grains in water under his microscope. The pollen grains appeared to be jiggling. Brown used Dalton's atomic theory to describe patterns in the way they moved. This was called "brownian motion". In 1905 Albert Einstein used mathematics to prove that the seemingly random movements were caused by the reactions of atoms, and by doing this he conclusively proved the existence of the atom.

In 1869, Russian scientist Dmitri Mendeleev published the first version of the periodic table. The periodic table groups elements by their atomic number (how many protons they have. This is usually the same as the number of electrons).

Elements in the same column, or period, usually have similar properties. For example, helium, neon, argon, krypton and xenon are all in the same column and have very similar properties. All these elements are gases that have no colour and no smell. Also, they are unable to combine with other atoms to form compounds. Together they are known as the noble gases.

The physicist J.J. Thomson was the first person to discover electrons. This happened while he was working with cathode rays in 1897. He realized they had a negative charge, unlike protons (positive) and neutrons (no charge). Thomson created the plum pudding model, which stated that an atom was like plum pudding: the dried fruit (electrons) were stuck in a mass of pudding (protons). In 1909, a scientist named Ernest Rutherford used the Geiger–Marsden experiment to prove that most of an atom is in a very small space called the atomic nucleus. Rutherford took a photo plate and covered it with gold foil, and then shot alpha particles (made of two protons and two neutrons stuck together) at it. Many of the particles went through the gold foil, which proved that atoms are mostly empty space. Electrons are so small they make up only 1% of an atom's mass.

In 1913, Niels Bohr introduced the Bohr model. This model showed that electrons travel around the nucleus in fixed circular orbits. This was more accurate than the Rutherford model. However, it was still not completely right. Improvements to the Bohr model have been made since it was first introduced.

In 1925, chemist Frederick Soddy found that some elements in the periodic table had more than one kind of atom.

For example, any atom with 2 protons should be a helium atom. Usually, a helium nucleus also contains two neutrons. However, some helium atoms have only one neutron. This means they truly are helium, because an element is defined by the number of protons, but they are not normal helium, either. Soddy called an atom like this, with a different number of neutrons, an "isotope". To get the name of the isotope we look at how many protons and neutrons it has in its nucleus and add this to the name of the element. So a helium atom with two protons and one neutron is called helium-3, and a carbon atom with six protons and six neutrons is called carbon-12. However, when he developed his theory Soddy could not be certain neutrons actually existed. To prove they were real, physicist James Chadwick and a team of others created the mass spectrometer. The mass spectrometer actually measures the mass and weight of individual atoms. By doing this Chadwick proved that to account for all the weight of the atom, neutrons must exist.

In 1937, German chemist Otto Hahn became the first person to create nuclear fission in a laboratory. He discovered this by chance when he was shooting neutrons at a uranium atom, hoping to create a new isotope. However, he noticed that instead of a new isotope the uranium simply changed into a barium atom, a smaller atom than uranium. Apparently, Hahn had "broken" the uranium atom. This was the world's first recorded nuclear fission reaction. This discovery eventually led to the creation of the atomic bomb.

Further into the 20th century, physicists went deeper into the mysteries of the atom. Using particle accelerators they discovered that protons and neutrons were actually made of other particles, called quarks.

The most accurate model so far comes from the Schrödinger equation. Schrödinger realized that the electrons exist in a cloud around the nucleus, called the electron cloud. In the electron cloud, it is impossible to know exactly where electrons are. The Schrödinger equation is used to find out where an electron is likely to be. This area is called the electron's orbital.

The complex atom is made up of three main particles; the proton, the neutron and the electron. The isotope of Hydrogen Hydrogen-1 has no neutrons, just the one proton and one electron. Protons have a positive electric charge and electrons have a negative charge. A positive hydrogen ion has no electrons, just the one proton. These two examples are the only known exceptions to the rule that all other atoms have at least one proton, one neutron and one electron each.

Electrons are by far the smallest of the three atomic particles, their mass and size is too small to be measured using current technology. They have a negative charge. Protons and neutrons are of similar size and weight to each other, protons are positively charged and neutrons have no charge.

Most atoms have a neutral charge; because the number of protons (positive) and electrons (negative) are the same, the charges balance out to zero. However, in ions (different number of electrons) this is not always the case, and they can have a positive or a negative charge. Protons and neutrons are made out of quarks, of two types; up quarks and down quarks. A proton is made of two up quarks and one down quark and a neutron is made of two down quarks and one up quark.

The nucleus is in the middle of an atom. It is made up of protons and neutrons. Usually in nature, two things with the same charge repel or shoot away from each other. So for a long time it was a mystery to scientists how the positively charged protons in the nucleus stayed together. They solved this by finding a particle called a "gluon". Its name comes from the word "glue" as gluons act like atomic glue, sticking the protons together using the "strong nuclear force". It is this force which also holds the quarks together that make up the protons and neutrons.

The number of neutrons in relation to protons defines whether the nucleus is stable or goes through radioactive decay. When there are too many neutrons or protons, the atom tries to make the numbers the same by getting rid of the extra particles. It does this by emitting radiation in the form of alpha, beta or gamma decay. Nuclei can change through other means too. Nuclear fission is when the nucleus splits into two smaller nuclei, releasing a lot of stored energy. This release of energy is what makes nuclear fission useful for making bombs and electricity, in the form of nuclear power.

The other way nuclei can change is through nuclear fusion, when two nuclei join together, or fuse, to make a heavier nucleus. This process requires extreme amounts of energy in order to overcome the electrostatic repulsion between the protons, as they have the same charge. Such high energies are most common in stars like our Sun, which fuses hydrogen for fuel.

Electrons orbit, or travel around, the nucleus. They are called the atom's "electron cloud". They are attracted towards the nucleus because of the electromagnetic force. Electrons have a negative charge and the nucleus always has a positive charge, so they attract each other.

Around the nucleus, some electrons are further out than others, in different layers. These are called "electron shells". In most atoms the first shell has two electrons, and all after that have eight. Exceptions are rare, but they do happen and are difficult to predict. The further away the electron is from the nucleus, the weaker the pull of the nucleus on it. This is why bigger atoms, with more electrons, react more easily with other atoms.

The electromagnetism of the nucleus is not strong enough to hold onto their electrons and atoms lose electrons to the strong attraction of smaller atoms.

Some elements, and many isotopes, have what is called an "unstable nucleus". This means the nucleus is either too big to hold itself together or has too many protons or neutrons. When this happens the nucleus has to get rid of the excess mass or particles. It does this through radiation. An atom that does this can be called "radioactive". Unstable atoms continue to be radioactive until they lose enough mass/particles that they become stable. All atoms above atomic number 82 (82 protons, lead) are radioactive.

There are three main types of radioactive decay; alpha, beta and gamma.

Every radioactive element or isotope has what is named a "half-life". This is how long it takes half of any sample of atoms of that type to decay until they become a different stable isotope or element. Large atoms, or isotopes with a big difference between the number of protons and neutrons will therefore have a long half life, because they must lose more neutrons to become stable.

Marie Curie discovered the first form of radiation. She found the element and named it radium. She was also the first female recipient of the Nobel Prize.

Frederick Soddy conducted an experiment to observe what happens as radium decays. He placed a sample in a light bulb and waited for it to decay. Suddenly, helium (containing 2 protons and 2 neutrons) appeared in the bulb, and from this experiment he discovered this type of radiation has a positive charge.

James Chadwick discovered the neutron, by observing decay products of different types of radioactive isotopes. Chadwick noticed that the atomic number of the elements was lower than the total atomic mass of the atom. He concluded that electrons could not be the cause of the extra mass because they barely have mass.

Enrico Fermi, used the neutrons to shoot them at uranium. He discovered that uranium decayed a lot faster than usual and produced a lot of alpha and beta particles. He also believed that uranium got changed into a new element he named hesperium.

Otto Hahn and Fritz Strassmann repeated Fermi's experiment to see if the new element hesperium was actually created. They discovered two new things Fermi did not observe. By using a lot of neutrons the nucleus of the atom would split, producing a lot of heat energy. Also the fission products of uranium were already discovered: thorium, palladium, radium, radon and lead.

Fermi then noticed that the fission of one uranium atom shot off more neutrons, which then split other atoms, creating chain reactions. He realised that this process is called nuclear fission and could create huge amounts of heat energy.

That very discovery of Fermi's led to the development of the first nuclear bomb code-named 'Trinity'.

Astronomy

Astronomy (from the Greek "astron" (ἄστρον) meaning "star" and "nomos" (nόμος) meaning "law") is the scientific study of celestial bodies such as stars, planets, comets, and galaxies. The imaginary patterns in the night sky are called constellations.

The objects studied include stars, galaxies, planets, moons, asteroids, comets and nebulae. Phenomena outside the Earth's atmosphere are also studied. That includes supernovae explosions, gamma ray bursts, and cosmic microwave background radiation. Astronomy concerns the development, physics, chemistry, meteorology and movement of celestial bodies, as well as the structure and development of the Universe.

Astronomy is one of the oldest sciences. Ancient Greek people used the positions of the stars to navigate, and to find when was the best time to plant crops. Astronomy is very similar to astrophysics. A related subject, cosmology, is concerned with studying the Universe as a whole, and the way the universe changed over time. Astronomy is not the same as "astrology", the belief that motion of the stars and the planets may affect human lives.

Since the 20th century there have been two main types of astronomy, "observational" and "theoretical" astronomy. Observational astronomy uses telescopes and cameras to "observe" or look at stars, galaxies and other astronomical objects. Theoretical astronomy uses maths and computer models to explain the observations and predict what might happen. Working together, theories predict what should happen and observations show whether the predictions work. The main work of astronomy is to explain puzzling features of the universe. For thousands of years the most important issue was the motions of planets; now many other topics are studied.

Early astronomers used only their eyes to look at the stars. They made maps of the constellations and stars for religious reasons and calendars to work out the time of year. Early civilisations such as the Maya people and the Ancient Egyptians built simple observatories and drew maps of the stars positions. They also began to think about the place of Earth in the universe. For a long time people thought Earth was the center of the universe, and that the planets, the stars and the sun went around it. This is known as geocentrism.

Ancient Greeks tried to explain the motions of the sun and stars by taking measurements. A mathematician named Eratosthenes was the first who measured the size of the Earth and proved that the Earth is a sphere. A theory by another mathematician named Aristarchus was, that the sun is in the center and the Earth is moving around it. This is known as heliocentrism. Only a few people thought it was right. The rest continued to believe in the "geocentric" model. Most of the names of constellations and stars come from Greeks of that time.

Arabic astronomers made many advancements during the Middle Ages including improved star maps and ways to estimate the size of the Earth. They also learned from the ancients by translating Greek books into Arabic.

During the renaissance a priest named Nicolaus Copernicus thought, from looking at the way the planets moved, that the Earth was not the center of everything. Based on previous works, he said that the Earth was a planet and all the planets moved around the sun. This brought back the old idea of heliocentrism. A physicist called Galileo Galilei built his own telescopes, and used them to look more closely at the stars and planets for the first time. He agreed with Copernicus. The Catholic Church decided that Galileo was wrong. He had to spend the rest of his life under house arrest. Heliocentric ideas were soon improved by Johannes Kepler and Isaac Newton who invented the theory of gravity.

After Galileo, people made better telescopes and used them to see farther objects such as the planets Uranus and Neptune. They also saw how stars were similar to our Sun, but in a range of colours and sizes. They also saw thousands of other faraway objects such as galaxies and nebulae.

The 20th century after 1920 saw important changes in astronomy.

In the early 1920s it began to be accepted that the galaxy in which we live, the Milky Way, is not the only galaxy. The existence of other galaxies was settled by Edwin Hubble, who identified the Andromeda nebula as a different galaxy. It was also Hubble who proved that the universe was expanding. There were many other galaxies at large distances and they are receding, moving away from our galaxy. That was completely unexpected.

In 1931, Karl Jansky discovered radio emission from outside the Earth when trying to isolate a source of noise in radio communications, marking the birth of radio astronomy and the first attempts at using another part of the electromagnetic spectrum to observe the sky. Those parts of the electromagnetic spectrum that the atmosphere did not block were now opened up to astronomy, allowing more discoveries to be made.

The opening of this new window on the Universe saw the discovery of entirely new things, for example pulsars, which sent regular pulses of radio waves out into space. The waves were first thought to be alien in origin because the pulses were so regular that it implied an artificial source.

The period after World War 2 saw more observatories where large and accurate telescopes are built and operated at good observing sites, normally by governments. For example, Bernard Lovell began radio astronomy at Jodrell Bank using leftover military radar equipment. By 1957, the site had the largest steerable radio telescope in the world. Similarly, the end of the 1960s saw the start of the building of dedicated observatories at Mauna Kea in Hawaii, a good site for visible and infra-red telescopes thanks to its high altitude and clear skies.

The next great revolution in astronomy was thanks to the birth of rocketry. This allowed telescopes to be placed in space on satellites.

Space telescopes gave access, for the first time in history, to the entire electromagnetic spectrum including rays that had been blocked by the atmosphere. The X-rays, gamma rays, ultraviolet light and parts of the infra-red spectrum were all opened to astronomy as observing telescopes were launched. As with other parts of the spectrum, new discoveries were made.

From 1970s satellites were launched to be replaced with more accurate and better satellites, causing the sky to be mapped in nearly all parts of the electromagnetic spectrum.

Discoveries broadly come in two types: bodies and phenomena. Bodies are things in the Universe, whether it is a planet like our Earth or a galaxy like our Milky Way. Phenomena are events and happenings in the Universe.

For convenience, this section has been divided by where these astronomical bodies may be found: those found around stars are solar bodies, those inside galaxies are galactic bodies and everything else larger are cosmic bodies.

Diffuse Objects:

Compact Stars:

Burst events are those where there is a sudden change in the heavens that disappears quickly. These are called bursts because they are normally associated with large explosions producing a "burst" of energy. They include:

Periodic events are those that happen regularly in a repetitive way. The name periodic comes from period, which is the length of time required for a wave to complete one cycle. Periodic phenomena include: