The Ancient Greeks contributed a lot to modern society‚ but the biggest contribution of them was their contributions to the field of science and mathematics. To start off‚ the Pythagorean theorem contributed a lot to the field of mathematics. What the Pythagorean theorem does is help us to calculate the lengths of the sides of right triangles. Secondly‚ Archimedes contributed a ton to both fields. One of the most famous things that Archimedes did was find out if a crown that the king had ordered
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Anmol Mehrotra Pythagorean triples Math Bonus A Pythagorean triple consists of three positive integers a ‚ b ‚ and c ‚ such 2 2 2 that a + b = c . Such a triple is commonly written ( a ‚ b ‚ c )‚ and a wellknown example is (3‚ 4‚ 5). If ( a ‚ b ‚ c ) is a Pythagorean triple‚ then so is ( ka ‚ kb ‚ kc ) for any positive integer k . A primitive Pythagorean triple is one in which a ‚ b
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Castle Rock‚ walk x paces to the north‚ and then walk 2x - 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? Given this scenario the Pythagorean Theorem would be the strategy we use to solve for x. I started off with the Pythagorean Theorem. I then plugged the binomials into the Pyth. Thrm. Next I moved (2+6)^2 to le left of the equation by subtracting (2x+6)^2 from both sides. I then squared the expression Next I foiled the expression
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Pythagoras is commonly known for his discovery of the “Pythagorean Theorem”. The Pythagorean thereom states that the‚ “Square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides: c2 = a2 + b2” (Pyhtagorean…). Without Pythagoreas or his invention we would not
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ANSWER: 8-4 Trigonometry Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A 3. cos A SOLUTION: The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. So‚ ANSWER: SOLUTION: The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So‚ 4. tan A ANSWER: 2. tan C SOLUTION: The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. So‚ ANSWER: 3. cos A SOLUTION:
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circle. In the 5th century AD Zu Chongzhi also used it to find the volume of a sphere. In the 12th century Bhaskara II of India developed an early derivative representing infinitesimal change and described an early form of “Rolle’s theorem”. Seki Kowa expanded the method of exhaustion in the early 17th century in Japan. In AD 1668 James Gregory provided a special case of the second fundamental theorem of calculus. Some applications of calculus are used by biologist‚ electrical engineers‚ architects
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Lesson 1: Trigonometric Functions of an Acute Angle c a b C A B The ratios of the lengths of the sides of a right triangle are called the trigonometric ratios. For convenience‚ we will name the three sides and three vertices of the right triangle as‚ a‚ b‚ and c for sides and the A‚ B‚ and C for the vertices as shown in the figure: Sine (sin) Function of an acute angle of a right triangle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse. Cosine (cos)
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History of science and technology in the Indian subcontinent * Outline of South Asian history * History of Indian subcontinent | Stone age (7000–3000 BC)[show] * Mehrgarh Culture (7000–3300 BC) | Bronze age (3000–1300 BC)[show] * Indus Valley Civilization (3300–1700 BC) * – Early Harappan Culture (3300–2600 BC) * – Mature Harappan Culture (2600–1900 BC) * – Late Harappan Culture (1700–1300 BC) * Ochre Coloured Pottery culture (from 2000 BC) * Swat culture (1600–500 BC) |
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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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figures. 9. Construct formal‚ logical arguments‚ proofs‚ and constructions. 10. Determine how changes in dimensions affect the perimeter‚ area‚ and volume of common geometric figures and solids. 11. State the Pythagorean Theorem and its converse. 12. Solve problems using the Pythagorean Theorem and its converse‚ and the properties of complementary‚ supplementary‚ vertical‚ and exterior angles. 13. Define the properties of complementary‚ supplementary‚ vertical‚ and exterior angles. 14. Compute the
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