Fermat's Last Theorem The 1670 edition of Diophantus' Arithmetica includes Fermat's commentary, particularly his "Last Theorem" (Observatio Domini Petri de Fermat). In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. Overview The claim eventually became one of the most notable unsolved problems of mathematics. The Pythagorean equation has an infinite number of positive integer solutions for a, b, and c; these solutions are known as Pythagorean triples. Subsequent developments and solution Mathematical history Pythagoras and Diophantus Pythagorean triples Examples of Pythagorean triples include (3, 4, 5) and (5, 12, 13).
Islam Islam (/ˈɪslɑːm/;[note 1] Arabic: الإسلام, al-ʾIslām IPA: [ælʔɪsˈlæːm] ( )[note 2]) is a monotheistic and Abrahamic religion articulated by the Qur'an, an Islamic holy book considered by its adherents to be the verbatim word of God (Allāh), and for the vast majority of adherents, also by the teachings and normative example (called the Sunnah and composed of hadith) of Muhammad (c. 570–8 June 632 CE), considered by most of them to be the last prophet of God. An adherent of Islam is called a Muslim. Most Muslims are of two denominations: Sunni (75–90%) or Shia (10–20%). About 13% of Muslims live in Indonesia, the largest Muslim-majority country, 25% in South Asia, 20% in the Middle East, and 15% in Sub-Saharan Africa. Sizable minorities are also found in Europe, China, Russia, and the Americas. Etymology and meaning Articles of faith God Main articles: God in Islam and Allah Islam's most fundamental concept is a rigorous monotheism, called tawḥīd (Arabic: توحيد). Angels
Philosophy Philosophy is the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational argument. In more casual speech, by extension, "philosophy" can refer to "the most basic beliefs, concepts, and attitudes of an individual or group". The word "philosophy" comes from the Ancient Greek φιλοσοφία (philosophia), which literally means "love of wisdom". The introduction of the terms "philosopher" and "philosophy" has been ascribed to the Greek thinker Pythagoras. Areas of inquiry Philosophy is divided into many sub-fields. These include epistemology, logic, metaphysics, ethics, and aesthetics. Some of the major areas of study are considered individually below. Epistemology Rationalism is the emphasis on reasoning as a source of knowledge. Logic
Osho Chandra Mohan Jain (11 December 1931 – 19 January 1990), also known as Acharya Rajneesh from the 1960s onwards, as Bhagwan Shree Rajneesh ( pronunciation ) during the 1970s and 1980s, and as Osho ( pronunciation ;) from 1989, was an Indian mystic, guru and spiritual teacher. His international following has continued after his death. A professor of philosophy, he traveled throughout India during the 1960s as a public speaker. Rajneesh's ashram in Pune is today known as the Osho International Meditation Resort. Biography Childhood and adolescence: 1931–1950 University years and public speaking: 1951–1970 In 1951, aged nineteen, Rajneesh began his studies at Hitkarini College in Jabalpur. Asked to leave after conflicts with an instructor, he transferred to D.N. After calling for a greater acceptance of sex in a 1968 lecture series (later published as From Sex to Superconsciousness), Rajneesh was dubbed "the sex guru" by the Indian press. Bombay: 1970–1974 Peter B.
Evolutionary origin of religions The evolutionary origin of religions theorizes about the emergence of religious behavior during the course of human evolution. Nonhuman religious behaviour Humanity’s closest living relatives are common chimpanzees and bonobos. These primates share a common ancestor with humans who lived between four and six million years ago. It is for this reason that chimpanzees and bonobos are viewed as the best available surrogate for this common ancestor. Barbara King argues that while non-human primates are not religious, they do exhibit some traits that would have been necessary for the evolution of religion. Marc Bekoff, Professor Emeritus of Ecology and Evolutionary Biology at the University of Colorado, Boulder, argues that many species grieve death and loss. Setting the stage for human religion Increased brain size Robin Dunbar argues that the critical event in the evolution of the neocortex took place at the speciation of archaic homo sapiens about 500,000 years ago.
Uncertainty principle where ħ is the reduced Planck constant. The original heuristic argument that such a limit should exist was given by Heisenberg, after whom it is sometimes named the Heisenberg principle. This ascribes the uncertainty in the measurable quantities to the jolt-like disturbance triggered by the act of observation. Though widely repeated in textbooks, this physical argument is now known to be fundamentally misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument; the formal mathematical result remains valid, however. Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Introduction Click to see animation. The superposition of several plane waves to form a wave packet. As a principle, Heisenberg's uncertainty relationship must be something that is in accord with all experience. . with yields where
Christianity Christianity is an Abrahamic religion that began as a Jewish sect in the mid-1st century. Originating in the Levant region of the Middle East, it quickly spread to Syria, Mesopotamia, Asia Minor and Egypt. It grew in size and influence over a few centuries, and by the end of the 4th century had become the official state church of the Roman Empire, replacing other forms of religion practiced under Roman rule. During the Middle Ages, most of the remainder of Europe was Christianized, and adherents were gained in the Middle East, North Africa, Ethiopia and parts of India. Following the Age of Discovery, Christianity spread to the Americas, Australasia, sub-Saharan Africa, and the rest of the world through missionary work and colonization. Christianity has played a prominent role in the shaping of Western civilization. Beliefs Creeds Its main points include: Ten Commandments These are quotes from Deuteronomy 6:4 and Leviticus 19:18.
Classical music Montage of some great classical music composers. From left to right: Top row: Antonio Vivaldi, Johann Sebastian Bach, George Frideric Handel, Wolfgang Amadeus Mozart, Ludwig van Beethoven; second row: Gioachino Rossini, Felix Mendelssohn, Frédéric Chopin, Richard Wagner, Giuseppe Verdi; third row: Johann Strauss II, Johannes Brahms, Georges Bizet, Pyotr Ilyich Tchaikovsky, Antonín Dvořák; bottom row: Edvard Grieg, Edward Elgar, Sergei Rachmaninoff, George Gershwin, Aram Khachaturian The term "classical music" did not appear until the early 19th century, in an attempt to distinctly canonize the period from Johann Sebastian Bach to Beethoven as a golden age. The earliest reference to "classical music" recorded by the Oxford English Dictionary is from about 1836. Characteristics Literature The most outstanding characteristic of classical music is that the repertoire tends to be written down in musical notation, creating a musical part or score. Instrumentation
Religion Pantheon List of Gods Roman PaganismThe religion of Rome If anything, the Romans had a practical attitude to religion, as to most things, which perhaps explains why they themselves had difficulty in taking to the idea of a single, all-seeing, all-powerful god. The origins of Roman Religion Most of the Roman gods and goddesses were a blend of several religious influences. It could even occur that a deity was worshipped, for reasons no-one really could remember. Prayer and Sacrifice Most form of religious activity required some kind of sacrifice. Prayer and Sacrifice Omens and Superstitions The Roman was by nature a very superstitious person. Omens and Superstitions Religion in the Home If the Roman state entertained temples and rituals for the benefit of the greater gods, then the Romans in the privacy of their own homes also worshipped their domestic deities. Religion in the Home Countryside Festivals To the Roman peasant the world around simply abound with gods, spirits and omens. The Festivals
Religion, World Religions, Comparative Religion - Just the facts on the world's religions.