PlatoPlato (ˈpleɪtoʊ ; Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an ancient Greek philosopher born in Athens during the Classical period in Ancient Greece. In Athens, Plato founded the Academy, a philosophical school where he taught the philosophical doctrines that would later become known as Platonism. Plato (or Platon) was a pen name derived, apparently, from the nickname given to him by his wrestling coach - allegedly a reference to his physical broadness.
Empirical evidenceEmpirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms evidence and empirical are to be defined. Often different fields work with quite different conceptions.
PhaedoPhædo or Phaedo (ˈfiːdəʊ; Φαίδων, Phaidōn phaídɔːn), also known to ancient readers as On The Soul, is one of the best-known dialogues of Plato's middle period, along with the Republic and the Symposium. The philosophical subject of the dialogue is the immortality of the soul. It is set in the last hours prior to the death of Socrates, and is Plato's fourth and last dialogue to detail the philosopher's final days, following Euthyphro, Apology, and Crito. One of the main themes in the Phaedo is the idea that the soul is immortal.
Stirling's approximationIn mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: where the big O notation means that, for all sufficiently large values of , the difference between and will be at most proportional to the logarithm.
Republic (Plato)The Republic (Politeia; De Republica) is a Socratic dialogue, authored by Plato around 375 BCE, concerning justice (δικαιοσύνη), the order and character of the just city-state, and the just man. It is Plato's best-known work, and one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates discusses the meaning of justice and whether the just man is happier than the unjust man with various Athenians and foreigners.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
