What the World Would Be Without Inventions?
Total Page:16
File Type:pdf, Size:1020Kb
What the world would be without inventions? GREEK INVENTORS THROUGH TIME “The introduction of noble inventions seems to hold by far the most excellent place among human actions” ~ Francis Bacon 7 Greek inventors through time • Archimides • Euclid • Pythagoras • Thucydides • Ctesibius of Alexandria • Constantin Carathéodory • George Papanikolaou Archimides, the great mathematician and inventor of the “Archimides principle” GREEK INVENTORS I Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης [ar.kʰi.mɛː.dɛ̂ːs]; c . 287 – c. 212 BC) was a Greek mathematician, physicist, en gineer, inventor, and astronomer. He is regarded as one of the leading scientists in classical antiquity. Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral. His other mathematical achievements include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. Archimedes' principle A metal bar, placed into a container of water on a scale, displaces as much water as its own volume, increasing the mass of the container's contents and weighing down the scale. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. "Eureka!“ While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα, heúrēka!, lit. 'I have found [it]!'). The test was conducted successfully, proving that silver had indeed been mixed in. The death of Archimides Archimedes died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year- long siege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. He was said to have implored the soldier not to destroy his work by the famous phrase “Do not disturb my circles!”. The soldier was enraged by this, and killed Archimedes with his sword. Nowadays, Archimides is considered to be the greatest mathematician of ancient history, and one of the greatest of all time. Euclid, the father of Geometry GREEK INVENTORS II Euclid (Ancient Greek: Εὐκλείδης – Eukleídēs, pronounced [eu̯ .kleː.dɛːs]; fl. 300 BC), was a Greek mathematician, often referred to as the "founder of geometry or the "father of geometry". The English name Euclid i s the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious”. If he came from Alexandria, he would have known the Serapeum of Alexandria, and the Library of Alexandria, and may have worked there during his time. Euclid's arrival in Alexandria came about ten years after its founding by Alexander the Great, which means he arrived c. 322 BC. He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especiall y geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigor. Euclid's Elements Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry." One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5. Euclid's construction of a regular dodecahedron. Construction of a dodecahedron by placing faces on the edges of a cube. Euclid in Rafaello’s “The School of Athens” Fresco, Vatican. Euclid’s statue in Oxford University Euclidean Geometry, the main Geometry corpus for Greek High School students. Pythagoras, the great mathematician and musician GREEK INVENTORS III Pythagoras of Samos (c. 570 BC – 495 BC) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Pythagoreanism Around 530 BC, Pythagoras travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism. Pythagoreans Celebrate the Sunrise (1869) by Fyodor Bronnikov Illustration from 1913 showing Pythagoras teaching a class of women. Many prominent members of his school were women and some modern scholars think that he may have believed that women should be taught philosophy as well as men. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones. Pythagoras is credited with having devised the tetractys, an important sacred symbol in later Pythagoreanism. The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations a nd thus resonate to produce an inaudible symphony of music. The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). Pythagoras’ influence Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses influenced the modern vegetarian movement. In Raphael's fresco The School of Athens, Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of a lyre above a drawing of the sacred tetractys. Thucidides, the father of scientific History GREEK INVENTORS IV Thucydides (Ancient Greek: Θουκυδίδης Thoukūdídēs [tʰuːkyːdídɛːs]; c. 460 – c. 400 BC) was an Athenian historian and general . His History of the Peloponnesian War recounts the fifth-century BC war between Sparta and Athens u ntil the year 411 BC. Thucydides has been dubbed the father of "scientific history" by those who accept his claims to have applied strict standards of impartiality and evidence-gathering and analysis of cause and effect, without reference to intervention by the deities, as outlined in his introduction to his work. The Peloponnesian War Thucydides identifies himself as an Athenian, telling us that his father's name was Olorus and that he was from the Athenian deme of Halimous. A somewhat doubtful anecdote of his early life still exists. While still a youth of 10-12 years, he and his father were supposed to have gone to the agora of Athens where the young Thucydides heard a lecture by the historian Herodotus.