EXT. PAGE’S DRIVEWAY - DAY PAGE‚ is a father. He is in his early 40s. He places a gift bag next to his daughters new car. He grabs a bow out of the bag and carefully places it on the hood of the car. Morris drives fast past Page’s house. He honks his horn. Page looks up at Morris who drives past him. He waves. PAGE Hi Morris. He focuses his attention back on making sure the bow looks perfect on his daughters car. INT. CESSNA 172 - DAY Morris puts his earmuffs on. He flips the control buttons
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Geometry (Greek γεωμετρία; geo = earth‚ metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modernmathematics‚ the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid‚ who introduced mathematical rigor and the axiomatic method still in use today. His book‚ The Elements is widely considered the most influential textbook
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was from 600 B.C.E to about 300 B.C.E. (Allen‚ 1997‚ para. 2). For the earliest period of Greek mathematics‚ there are few primary sources of information. We are therefore forced to rely extensively on the Euclidean Summary of Proclus. This contains an outline of the development of Greek geometry from early times until Euclid (Allen‚ 1997). Thales is often considered to be one of the first Greek mathematicians. The proposition known as the “Theorem of Thales” states‚ “The diameter of a circle always
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JTG- Ch.2 Euclid’s Proof of the Pythagorean Theorem Century and a half between Hippocrates and Euclid. Plato esteemed geometry to be the entrance to his Academy. Let no man ignorant of geometry enter here. “Logical scandal” Theorems were believed to be correct as stated but they lacked the material to prove them. Euclid’s Elements was said to become the staple of mathematics or the standard. 13 books‚ 465 propositions (not all Euclid but rather a collection of great mathematicians
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Topic 1- Mathematics and Certainty Having said something about the nature of formal systems‚ we must now look in more detail at the nature of mathematical certainty. To do this‚ let us begin by making two distinctions. The first concerns the nature of propositions. An analytic proposition is one that is true by definition. A synthetic proposition is any proposition that is not analytic. So we can say that every proposition is either analytic or synthetic. The second distinction concerns how we
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accepted axioms. An example that was often used to illustrate this was Euclidean geometry. When you have the five axioms defined and the postulates formed from the axioms you have basic geometry that you learned in high school (Euclidean). However you learn later on in the book‚ that if you ignore the 5th axiom than you have a whole new kind of geometry‚ called non-Euclidean geometry. What everyone thought they knew about geometry and axioms was completely changed by altering the original axiom. That
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Euclid of Alexandria. His fame comes from his writings‚ in particular his masterpiece‚ The Elements‚ the long studied thirteen volume work on geometry and number theory. Except for the Bible‚ no other book has been so widely translated and circulated. It is undoubtedly the best mathematic text ever written and made him known to all as "the father of geometry."� As legendary as his work is to the world‚ his personal like if just the opposite. There is very little known about his life. In fact‚ his
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lived in the time of the first Ptolemy; for Archimedes‚ who followed closely upon the first Ptolemy makes mention of Euclid‚ and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements‚ to which he replied that there was no royal road to geometry. He is therefore younger than Plato’s circle‚ but older than Eratosthenes and Archimedes; for these were contemporaries‚ as Eratosthenes somewhere says. In his aim he was a Platonist‚ being in sympathy with
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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.[1][2][3] In the Elements‚ Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote
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and geometry playing equal parts. In a similar manner‚ algebraic formulas can also be derived from geometric diagrams. A good example would be the conics. One can’t imagine the conics without their respective geometric diagrams. Not only is geometry tied into algebra in that sense‚ but the fact that the curves had been under scrutiny by the Greeks‚ the greatest exponents of geometry‚ shows their inclination toward some algebra. Numerical approximations for pi also heavily featured geometry in
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