PDF-Ellipses and hyperbolas of decomposition of even numbers into pairs of prime numbers

This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbolabrCertain pairs of prime numbers can be represented as radiusdistances from the focuses to points lying either on the ellipse or on the hyperbolabrThe ellipse equation can be written in the following form pk pt 2nbrThe hyperbola equation can be written in the following form pk pt 2nbrHere pk and pt are prime numbers p1 2 p2 3 p3 5 p4 7brk and t are indices of prime numbersbr2n is a given even numberbrk t n NbrIf we construct ellipses and hyperbolas based on the above we get the followingbr1 there are only 5 nonintersecting curves for 2n4 2n6 2n8 2n10 2n16 The remaining ellipses have intersection pointsbr2 there is only 1 nonintersecting hyperbola for 2n2 and 1 nonintersecting vertical line The remaining hyperbolas have intersection pointsbrWill there be any new thoughts ideas about this. Academic Essays. Green Hope Honor Code. Cheating: Numerous behaviors will be considered cheating. Some of these areas include, but are not limited to, the following: using cheat sheets; using former students’ notebooks; using internet resources without citing them as appropriate sources; misrepresenting something as being real and actual; using cell phones to create images of tests, quizzes, and/or other assignments; and text messaging with other students regarding a test or quiz. The use of technology in cheating can occur on small assignments such as homework assignments as well as on more formal tests, essays, and projects. Students can be guilty of cheating if they give out or are in receipt of the material.. Date: ____________. Ellipses. Standard Equation of an Ellipse. Center at (0,0). x. 2. a. 2. y. 2. b. 2. +. = 1. y. x. (–. a. , 0). . (. a. , 0). . (0, . b. ). (0, –. b. ). O. Horizontal Major Axis. A UWF Writing Lab Mini . Lesson. Mini-Lesson #63. DEFINITION. ELLIPSIS: a . punctuation mark . of three spaced dots (. . .) used to show an omission in writing or printing (Plural: . ellipses. ). Uses of Ellipses. Hyperbola: a set of all points (x, y) the difference of whose distances from two distinct fixed points (. foci. ) is a positive constant. . Similar to ellipse, which is the SUM of distances. Every hyperbola has two disconnected branches. The line through the foci intersects a hyperbola at its two . Date: ______________. Horizontal. transverse axis:. 9.5 Hyperbolas. x. . 2. a. 2. y. 2. b. 2. –. = 1. y. x. V. 1. (–. a. , 0). V. 2. (. a. , 0). Hyperbolas with Center (0,0). asymptotes: . y. = ± . by Carol Edelstein. Definition. Product. – An answer to a multiplication problem.. . 7 x 8 = 56. Product. Definition. Factor. – a number that is multiplied by another to give a product.. . 7 x 8 = 56. This is it, the final grammar notes for the rest of the school year. . Dashes. Like commas, semicolons, colons, and ellipses, the dash represents an . interrupton. , or an abrupt change of thought. . Basic hyperbola vocab. Hyperbola. : Set of all points P such that the . difference. of the distance between P and two fixed points (foci) is a constant. Vertices. : The line through the foci intersects the hyperbola at the vertices. Learning Goals. We will use our divisibility rules so that we can decompose numbers into prime factors.. We’ll know we understand when we can identify the prime factors that are used to form a number.. There is a rule for finding any prime (. eg. the . ). . There . is a way to find out how many primes are below any number (. eg. Number of primes below 1000). . There . is no end to the prime numbers. . What’s a Prime Number?. Lots of definitions out there. My Favorite (recursive): . “an integer greater than 1, that is not divisible by any smaller primes”. Note: The above is equivalent to (but feels less restrictive than) the more standard: . The Ellipse. Basic oval. Has a center point, 2 foci, focal axis, and 2 vertices on the focal axis. https://. www.youtube.com/watch?v=7UD8hOs-vaI. The ellipse. The ellipse: formulas. Ellipses with center (0, 0). by Carol Edelstein. Definition. Product. – An answer to a multiplication problem.. . 7 x 8 = 56. Product. Definition. Factor. – a number that is multiplied by another to give a product.. . 7 x 8 = 56. Seth Futrell, Matthew Ritchie, . Dakota Perryman, Mark Thompson . (Tag’s Tots). Background History . Prime numbers have fascinated the human race for millennia with solutions to finding primes predating the times of euclid. Primes continue to amaze mathematicians and theoretical thinkers daily. Research of these fascinating numbers continues in present day with the continuing growth of the field of number theory and encryption protocols ..