Pythagoreanism

Pythagoreanism originated in the 6th century BCE, based on teachings, or beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism. Pythagorean ideas exercised a marked influence on Aristotle, and Plato, and through them, all of Western philosophy.

Historians from the Stanford Encyclopedia of Philosophy pointed out

Two schools

According to tradition, pythagoreanism developed at some point into two separate schools of thought, the mathēmatikoi (μαθηματικοί, Greek for "Teachers") and the akousmatikoi (ἀκουσματικοί, Greek for "listeners").

John Burnet (1892) noted

According to Iamblichus (ca. 250-330 AD, 1918 translation) in The life of Pythagoras, by Thomas Taylor

Excerpt from a speech by the character ‘Aristotle’ in Protrepticus (Hutchinson and Johnson, 2015)

History

According to historians like Thomas Gale (based on Archytas account), Thomas Taler (based on the work of Iamblichus), or Cantor, Archytas (428 BC) became the head of the school, about a century after the murder of Pythagoras. According to August Böckh (1819), who cites Nicomachus, Philolaus was the successor of Pythagoras. And according to Cicero (de Orat. III 34.139), Philolaus was teacher of Archytas of Tarentum.

Pythagoras

Pythagoras of Samos (US /pɪˈθæɡərəs/;UK /paɪˈθæɡərəs/;Greek: Πυθαγόρας ὁ Σάμιος Pythagóras ho Sámios "Pythagoras the Samian", or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek; c. 570 – c. 495 BC) was an Ionian Greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and traveled, visiting Egypt and Greece, and maybe India, and in 520 BC returned to Samos. Around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild.

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.

Khan Academy

Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.

History

The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.

In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.

Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof.There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.

All Ages

All Ages is a compilation album by the American punk rock band Bad Religion. It was released on November 7, 1995 through Epitaph Records. The compilation contains songs from How Could Hell Be Any Worse? to Generator, and two live tracks recorded during their 1994 European tour, which were the first tracks to feature guitarist Brian Baker.

Background

All Ages contains material from six of Bad Religion's first seven studio albums released on Epitaph, omitting songs from the band's second album Into the Unknown and their seventh album Recipe for Hate; however, "American Jesus" from Recipe for Hate was included on the Japanese edition. It also contains no tracks from the Bad Religion and Back to the Known EPs. The band had left Epitaph for Atlantic in 1993, where they reissued Recipe for Hate and began to experience major worldwide commercial success.

The live tracks "Do What You Want" and "Fuck Armageddon... This Is Hell" were recorded live at the Karen Klub in Goteborg, Sweden on October 8, 1994 on Bad Religion's Stranger than Fiction tour. These tracks were the first to feature guitarist Brian Baker, who had replaced Brett Gurewitz before the release of Stranger than Fiction.