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Mathematicians
Often, to completely understand the importance of a mathematical theory, it's essential to know about the person who developed it. This category is where all questions about historically significant mathematicians should be asked.
6,570 Questions
How did Descartes think of the coordinate planes?
It is said that he was ill and in bed. He looked up at the ceiling where he noticed a fly. He figured out that knowing the distances from a corner of the ceiling along the two adjacent sides of the ceiling will uniquely identify its location. So, if the corner of the ceiling was the origin and the two adjacent sides were the axes, you have the Cartesian plane.
Did Rene Descartes have a wife and children?
Rene Descartes has not married but had an illegitimate daughter Francine who died at the young age of 5 due to a fever. He had decided take control for her education but 'passed' her as his niece.
What awards did René Descartes receive?
René Descartes, often called the father of modern philosophy, attempted to break with the philosophical traditions of his day and start philosophy anew. Rejecting the Aristotelian philosophy of the schools, the authority of tradition and the authority of the senses, he built a philosophical system that included a method of inquiry, a metaphysics, a mechanistic physics and biology, and an account of human psychology intended to ground an ethics. Descartes was also important as one of the founders of the new analytic geometry, which combines geometry and algebra, and whose certainty provided a kind of model for the rest of his philosophy.
After an education in the scholastic and humanistic traditions, Descartes' earliest work was mostly in mathematics and mathematical physics, in which his most important achievements were his analytical geometry and his discovery of the law of refraction in optics. In this early period he also wrote his unfinished treatise on method, the Rules for the Direction of the Mind, which set out a procedure for investigating nature, based on the reduction of complex problems to simpler ones solvable by direct intuition. From these intuitively established foundations, Descartes tried to show how one could then attain the solution of the problems originally posed.
Descartes abandoned these methodological studies by 1628 or 1629, turning first to metaphysics, and soon afterwards to an orderly exposition of his physics and biology in The World. But this work was overtly Copernican in its cosmology, and when Galileo was condemned in 1633, Descartes withdrew The Worldfrom publication; it appeared only after his death.
Descartes' mature philosophy began to appear in 1637 with the publication of a single volume containing the Geometry, Dioptrics and Meteors, three essays in which he presented some of his most notable scientific results, preceded by the Discourse on the Method, a semi-autobiographical introduction that outlined his approach to philosophy and the full system into which the specific results fit. In the years following, he published a series of writings in which he set out his system in a more orderly way, beginning with its metaphysical foundations in the Meditations (1641), adding his physics in the Principles of Philosophy (1644), and offering a sketch of the psychology and moral philosophy in the Passions of the Soul (1649).
In our youth, Descartes held, we acquire many prejudices which interfere with the proper use of our reason. Consequently, later we must reject everything we believe and start anew. Hence the Meditations begins with a series of arguments intended to cast doubt upon everything formerly believed, and culminating in the hypothesis of an all-deceiving evil genius, a device to keep former beliefs from returning. The rebuilding of the world begins with the discovery of the self through the 'Cogito Argument' ('I am thinking, therefore I exist') - a self known only as a thinking thing, and known independently of the senses. Within this thinking self, Descartes discovers an idea of God, an idea of something so perfect that it could not have been caused in us by anything with less perfection than God Himself. From this he concluded that God must exist which, in turn, guarantees that reason can be trusted. Since we are made in such a way that we cannot help holding certain beliefs (the so-called 'clear and distinct' perceptions), God would be a deceiver, and thus imperfect, if such beliefs were wrong; any mistakes must be due to our own misuse of reason. This is Descartes' famous epistemological principle of clear and distinct perception. This central argument in Descartes' philosophy, however, is threatened with circularity - the Cartesian Circle - since the arguments that establish the trustworthiness of reason (the Cogito Argument and the argument for the existence of God) themselves seem to depend on the trustworthiness of reason.
Also central to Descartes' metaphysics was the distinction between mind and body. Since the clear and distinct ideas of mind and body are entirely separate, God can create them apart from one another. Therefore, they are distinct substances. The mind is a substance whose essence is thought alone, and hence exists entirely outside geometric categories, including place. Body is a substance whose essence is extension alone, a geometric object without even sensory qualities like colour or taste, which exist only in the perceiving mind. We know that such bodies exist as the causes of sensation: God has given us a great propensity to believe that our sensations come to us from external bodies, and no means to correct that propensity; hence, he would be a deceiver if we were mistaken. But Descartes also held that the mind and body are closely united with one another; sensation and other feelings, such as hunger and pain, arise from this union. Sensations cannot inform us about the real nature of things, but they can be reliable as sources of knowledge useful to maintaining the mind and body unity. While many of Descartes' contemporaries found it difficult to understand how mind and body can relate to one another, Descartes took it as a simple fact of experience that they do. His account of the passions is an account of how this connection leads us to feelings like wonder, love, hatred, desire, joy and sadness, from which all other passions derive. Understanding these passions helps us to control them, which was a central aim of morality for Descartes.
Descartes' account of body as extended substance led to a physics as well. Because to be extended is to be a body, there can be no empty space. Furthermore, since all body is of the same nature, all differences between bodies are to be explained in terms of the size, shape and motion of their component parts, and in terms of the laws of motion that they obey. Descartes attempted to derive these laws from the way in which God, in his constancy, conserves the world at every moment. In these mechanistic terms, Descartes attempted to explain a wide variety of features of the world, from the formation of planetary systems out of an initial chaos, to magnetism, to the vital functions of animals, which he considered to be mere machines.
Descartes never finished working out his ambitious programme in full detail. Though he published the metaphysics and the general portion of his physics, the physical explanation of specific phenomena, especially biological, remained unfinished, as did his moral theory. Despite this, however, Descartes' programme had an enormous influence on the philosophy that followed, both within the substantial group that identified themselves as his followers, and outside.
How did the Pythagoras contribute to ancient music theory?
It is highly probable that the Greek initiates gained their knowledge of the philosophic and therapeutic aspects of music from the Egyptians, who, in turn, considered Hermes the founder of the art. According to one legend, this god constructed the first lyre by stretching strings across the concavity of a turtle shell. Both Isis and Osiris were patrons of music and poetry. Plato, in describing the antiquity of these arts among the Egyptians, declared that songs and poetry had existed in Egypt for at least ten thousand years, and that these were of such an exalted and inspiring nature that only gods or godlike men could have composed them. In the Mysteries the lyre was regarded as the secret symbol of the human constitution, the body of the instrument representing the physical form, the strings the nerves, and the musician the spirit. Playing upon the nerves, the spirit thus created the harmonies of normal functioning, which, however, became discords if the nature of man were defiled.
While the early Chinese, Hindus, Persians, Egyptians, Israelites, and Greeks employed both vocal and instrumental music in their religious ceremonials, also to complement their poetry and drama, it remained for Pythagoras to raise the art to its true dignity by demonstrating its mathematical foundation. Although it is said that he himself was not a musician, Pythagoras is now generally credited with the discovery of the diatonic scale. Having first learned the divine theory of music from the priests of the various Mysteries into which he had been accepted, Pythagoras pondered for several years upon the laws governing consonance and dissonance. How he actually solved the problem is unknown, but the following explanation has been invented.
One day while meditating upon the problem of harmony, Pythagoras chanced to pass a brazier's shop where workmen were pounding out a piece of metal upon an anvil. By noting the variances in pitch between the sounds made by large hammers and those made by smaller implements, and carefully estimating the harmonies and discords resulting from combinations of these sounds, he gained his first clue to the musical intervals of the diatonic scale. He entered the shop, and after carefully examining the tools and making mental note of their weights, returned to his own house and constructed an arm of wood so that it: extended out from the wall of his room. At regular intervals along this arm he attached four cords, all of like composition, size, and weight. To the first of these he attached a twelve-pound weight, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight. These different weights corresponded to the sizes of the braziers' hammers.
Pythagoras thereupon discovered that the first and fourth strings when sounded together produced the harmonic interval of the octave, for doubling the weight had the same effect as halving the string. The tension of the first string being twice that of the fourth string, their ratio was said to be 2:1, or duple. By similar experimentation he ascertained that the first and third string produced the harmony of the diapente, or the interval of the fifth. The tension of the first string being half again as much as that of the third string, their ratio was said to be 3:2, or sesquialter. Likewise the second and fourth strings, having the same ratio as the first and third strings, yielded a diapente harmony. Continuing his investigation, Pythagoras discovered that the first and second strings produced the harmony of the diatessaron, or the interval of the third; and the tension of the first string being a third greater than that of the second string, their ratio was said to be 4:3, or sesquitercian. The third and fourth strings, having the same ratio as the first and second strings, produced another harmony of the diatessaron. According to Iamblichus, the second and third strings had the ratio of 8:9, or epogdoan.
The key to harmonic ratios is hidden in the famous Pythagorean tetractys, or pyramid of dots. The tetractys is made up of the first four numbers--1, 2, 3, and 4--which in their proportions reveal the intervals of the octave, the diapente, and the diatessaron. While the law of harmonic intervals as set forth above is true, it has been subsequently proved that hammers striking metal in the manner
How do you count to ten in Jamaican?
Here are the numbers 1-10 in Zulu: 1 - one - kunye 2 - two - kubili 3 - three - kuthathu 4 - four - kune 5 - five - kuhlanu 6 - six - yisithupa 7 - seven - yisikhombisa 8 - eight - yisishiyagalombili 9 - nine - yisishiyagalolunye 10 - ten - yishum
What mathamatic symbol did Rene Descartes invent?
The one known by most the the self-named Descartes' Theorem, in where it explains the relationship of Four mutually tangent circles. Descartes' first addressed this theorem in a letter to Princess Elizabeth of Bohemia.
http://www.usna.edu/Users/math/meh/euler.html that is a website on him Leonhard Euler was a Swiss mathematician who made extensive contributions to a wide range of mathematics and physics. Euler is also the name of a type of mathematical software.
Eulers rule is: F+V-2=E f=faces, v=verticies, e=edges
What are the contributions of Rene descartes?
== == Rene Descartes introduced the Cartesian coordinate system to mathematics, and made several notable contributions to the studies of imaginary numbers and trig functions.
two of the contributions of Rene Descartes was his analytical geometry and his theory of vortices.
What is Charles Babbage's birthday?
Charles Babbage, a British mathematician and original thinker, was the inventor of the first mechanical computing machine, called the 'Difference Engine'. He has often been referred to, quite rightly, as the 'Pioneer of the computer'.
What is the de Morgan's first theorem?
DeMorgan's Theorems are:
1. ~(A&B) ~A&~B.
For example:
"It's not raining and cold" means the same as "It is either not raining, or it is not cold", and
"It's not either raining or cold" means the same as "It's not raining and it's not cold".
Applied recursively, DeMorgan's theorem means that to find the inverse of a complex sentence, change all atoms to their inverses, and change all ANDs to ORs and ORs to ANDs.
What is the gcf of 129 133 and 215?
The Greatest Common Factor (GCF) of the numbers 129,133,215 is 1 because 1 is the greatest number that divides evenly into all of them.
What were the greatest architectural achievements of the Baroque era?
Baroque era is the building style of the Baroque era that began in the late 16th century. The Catholic church was first built during this era. It is also a embellishment of the wealth and power of the church.
Name any two Indian mathematician?
Here is few from ancient times: * Brahmagupta (c. 598-c. 670) * Govindaswami (c. 800-850) * Mahavira (Mahaviracharya) (850) * Pruthudakaswami (850) * Sridhara (900) * Manjula (930) * Aryabhata II (950) * Prashastidhara (958) * Halayudha (975) * Jayadeva (1000) * Sripathi (1039) * Hemachandra Suri (b. 1089) * Bhaskara (1114-c. 1185) * Cangadeva (1205) * Madhava of Sangamagramma (c. 1340-1425) * Narayama Pandit (1350) * Paramesvara (1360-1455) * Nilakantha Somayaji (1455-1555) * Sankara Variar (c. 1500-1560) * Narayana (c. 1500-1575) * Jyesthadeva (550) * Acyuta Pisarati (c. 1550-1621) * Putumana Somayaji (c. 1660-1740) * Jaganath Pandit (1700) * Sankara Varman (1800)
How can you convince your mother to tell you the name of your real father?
- Nothing. That's a privacy issue. Unless the person is collecting governmental funds for child support, etc. they cannot be forced to divulge such information. Another exception might possibly be if the child's life was endangered due to a possible genetic disease.
- If you are no longer a minor then hire a detective. They do this often in Canada.
Did Archimedes have any friends or family?
Most likely, although not for certain, Archimedes' father was an astronomer named Phidias and two of his friends were Conon of Samos and Eratosthenes of Cyrene. My source is linked below.
How much money do a investor make a year?
That depends on exactly how much money he has invested and how well he picked his investments. Had he been a real estate investor during 2007, he could have lost most of his money. But if he had invested all his money in wheat futures contracts during the summer, he could have doubled his money by December.
How did Leonardo Fibonacci die?
Leonardo Pisano Bogollo, known as Fibonacci, lived from c.1170 until c.1250. No one knows exactly how he died, but given his age, he probably died a natural death
How Rene descartes discover cartesian plane?
Descartes worked on the idea for the Cartesian coordinate system over the course of many years. His writings, including "Geometry", which was published in 1637, outlined the idea of the Cartesian coordinate system.
What was Rene' Descartes accomplishments?
René Descartes (March 31, 1596 - February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. While most notable for his groundbreaking work in philosophy, he has achieved wide fame as the inventor of the Cartesian coordinate system, which influenced the development of modern calculus.
The Islamic scientist and mathematician al-khowarizmi is credited with coining what word?
Al-jabr - the Arabic phrase we Anglicise to Algebra. He didn't invent the word itself, but the use of it.
