60. Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry". 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 (especially geometry) from the time of its publication until the late 19th or early 20th century. In the 'Elements', Euclid deduced the principles 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 rigor.
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.
There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the' Elements' was from Proclus, who briefly in his Commentary on the 'Elements' ascribes Euclid as its author.
Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid-Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.
Hi bobbym and math9maniac,
The solution #2708 is correct, bobbym and math9maniac! Excellent!
The problem #2707 may be treated as 'Null and Void'!
#2709. A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is
(i) other than an ace
(ii) a ten
(iii) a spade
(iv) a black card
59. Aristotle (384-322 BC) was a Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, whereafter Proxenus of Atarneus became his guardian. At eighteen, he joined Plato's Academy in Athens and remained there until the age of thirty-seven (c. 347 BC). His writings cover many subjects – including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theater, music, rhetoric, linguistics, politics and government – and constitute the first comprehensive system of Western philosophy. Shortly after Plato died, Aristotle left Athens and, at the request of Philip of Macedon, tutored Alexander the Great starting from 343 BC. According to the Encyclopædia Britannica, "Aristotle was the first genuine scientist in history ... [and] every scientist is in his debt."
Teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books. The fact that Aristotle was a pupil of Plato contributed to his former views of Platonism, but, following Plato's death, Aristotle immersed himself in empirical studies and shifted from Platonism to empiricism. He believed all peoples' concepts and all of their knowledge was ultimately based on perception. Aristotle's views on natural sciences represent the groundwork underlying many of his works.
Aristotle's views on physical science profoundly shaped medieval scholarship. Their influence extended into the Renaissance and were not replaced systematically until the Enlightenment and theories such as classical mechanics. Some of Aristotle's zoological observations, such as on the hectocotyl (reproductive) arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic.
In metaphysics, Aristotelianism profoundly influenced Judeo-Islamic philosophical and theological thought during the Middle Ages and continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. Aristotle was well known among medieval Muslim intellectuals and revered as "The First Teacher".
His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his literary style as "a river of gold" – it is thought that only around a third of his original output has survived.
58. Captain James Cook (7 November 1728 – 14 February 1779) was a British explorer, navigator, cartographer, and captain in the Royal Navy. Cook made detailed maps of Newfoundland prior to making three voyages to the Pacific Ocean, during which he achieved the first recorded European contact with the eastern coastline of Australia and the Hawaiian Islands, and the first recorded circumnavigation of New Zealand.
Cook joined the British merchant navy as a teenager and joined the Royal Navy in 1755. He saw action in the Seven Years' War, and subsequently surveyed and mapped much of the entrance to the Saint Lawrence River during the siege of Quebec. This helped bring Cook to the attention of the Admiralty and Royal Society. This notice came at a crucial moment in both Cook's career and the direction of British overseas exploration, and led to his commission in 1766 as commander of HM Bark Endeavour for the first of three Pacific voyages.
In three voyages Cook sailed thousands of miles across largely uncharted areas of the globe. He mapped lands from New Zealand to Hawaii in the Pacific Ocean in greater detail and on a scale not previously achieved. As he progressed on his voyages of discovery he surveyed and named features, and recorded islands and coastlines on European maps for the first time. He displayed a combination of seamanship, superior surveying and cartographic skills, physical courage and an ability to lead men in adverse conditions.
Cook was killed in Hawaii in a fight with Hawaiians during his third exploratory voyage in the Pacific in 1779. He left a legacy of scientific and geographical knowledge which was to influence his successors well into the 20th century and numerous memorials worldwide have been dedicated to him.
The solution #2706 is correct! Neat work!
#2707. Points A and B km apart from each other on a highway. A car starts from 'A' and another from 'B' at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. Find their speeds.
The solution #2703 is correct! Excellent!
#2704. A jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is 1/3, and the probability of selecting a green marble at random is 4/9. How many white marbles does the jar contain?
#5797. World Cancer Day is marked to raise awareness of cancer and to encourage its prevention, detection, and treatment. World Cancer Day was founded by the Union for International Cancer Control (UICC) to support the goals of the World Cancer Declaration, written in 2008. The primary goal of the World Cancer Day is to significantly reduce illness and death caused by cancer by 2020. When is the day?
#5798. International Women's Day (IWD), originally called International Working Women's Day, is celebrated every year. In different regions the focus of the celebrations ranges from general celebration of respect, appreciation, and love towards women to a celebration for women's economic, political, and social achievements. Started as a Socialist political event, the holiday blended the culture of many countries, primarily in Europe, especially those in the Soviet Bloc. Which day is it celebrated?
#5795. Who was/is Canaletto?
#5796. Name the style of 'les Fauves' (French for "the wild beasts"), a loose group of early twentieth-century Modern artists whose works emphasized painterly qualities and strong color over the representational or realistic values retained by Impressionism.