{"id":1019,"date":"2020-03-03T20:18:08","date_gmt":"2020-03-03T20:18:08","guid":{"rendered":"http:\/\/ibalmaths.com\/?page_id=1019"},"modified":"2020-03-14T08:24:34","modified_gmt":"2020-03-14T08:24:34","slug":"maths-exploration-ia-ideas","status":"publish","type":"page","link":"https:\/\/ibalmaths.com\/index.php\/maths-exploration-ia-ideas\/","title":{"rendered":"Maths Exploration (IA) ideas"},"content":{"rendered":"
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  1. Predicting fire spread in wildlife fields<\/a>: This mathematical model of fire presented in this paper offers for the first time a method for making quantitative evaluation of both rate of spread and fire intensity in fuels that qualify for the assumptions made on the model.\u00a0 The model didn’t use any prior knowledge of a fuel’s burning characteristic. It used only physical & chemical makeup of the fuel and the conditions in which it is expected to burn.<\/span><\/li>\r\n\t
  2. Butterfly network in Computer Algorithm<\/a>: A butterfly network is a blocking network and it does not allow an arbitrary connection of N inputs to N outputs without conflict. The butterfly network is modified in Benz network. The Benz network is a non-blocking network and it is generated by joining two butterfly networks back to back, in such a manner that data flows forward through one and in reverse through the other.<\/span><\/li>\r\n\t
  3. Mercator\u2019s Projection<\/a>: The\u00a0Mercator projection<\/strong>is a\u00a0cylindrical map projectionpresented by the\u00a0Flemish\u00a0geographer and cartographer\u00a0Gerardus Mercator\u00a0in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant\u00a0course\u00a0as straight segments that conserve the angles with the meridians.<\/span><\/li>\r\n\t
  4. Catenary Curve<\/a>: The catenary is the shape of a perfectly flexible chain suspended by its ends and acted on by gravity. The catenary is the locus of the focus of a parabola\u00a0rolling along a straight line. What makes the catenary arch important is its ability to withstand weight.\u00a0For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve.<\/span><\/li>\r\n\t
  5. Cissoid of Dicoles<\/a>: Diocles(~250 \u2013 ~100 BC) invented this curve to solve the\u00a0doubling the cubeproblem. The name cissoid (ivy-shaped) came from the shape of the curve. Later the method used to generate this curve is generalized, and we call curves generated this way as\u00a0cissoids.<\/span><\/li>\r\n\t
  6. Visual acuity<\/a>: Comparison of Monoyar chart\/Snellen chart\/Jaggers chart\/ Rosenbaum chart<\/span><\/li>\r\n\t
  7. Affine Transformation<\/a>: Affine transformationis a linear mapping method that preserves points, straight lines, and planes. Sets of parallel lines remain parallel after an affine transformation.<\/span><\/li>\r\n\t
  8. Liu Hui\u2019s \u03c0 inequality<\/a>: Liu Hui proved an inequality involving\u00a0\u03c0by considering the area of inscribed polygons with\u00a0N<\/em>and 2N<\/em>\u00a0sides.<\/span><\/li>\r\n\t
  9. Binet\u2019s Formula<\/a>: Binet’s formula\u00a0is an explicit formula used to find the\u00a0 th term of the Fibonacci sequence.<\/span><\/li>\r\n\t
  10. Omar Khayyam\u2019s solution of a cubic equation<\/a>: To contemporary students, a geometric solution to a cubic equation may seem strange. Exploring this approach poses a challenge of communicating how geometric problems motivated the study of cubic equations.<\/span><\/li>\r\n\t
  11. Bernstein Polynomial<\/a>: Expansions in Bernstein polynomials have a slow rate of convergence. For that reason, following Bernstein\u2019s application to the Weierstrass theorem, these polynomials had little impact in numerical analysis.<\/span><\/li>\r\n\t
  12. Four-color theorem<\/a>: The\u00a0four color theorem<\/strong>states that any map–a division of the plane into any number of regions–can be colored using no more than four colors in such a way that no two adjacent regions share the same color. A four color theorem is particularly notable for being the first major theorem proved by a computer.<\/span><\/li>\r\n\t
  13. Stoke\u2019s theorem<\/a>: Stokes’ theoremrelates a\u00a0surface integralof a the\u00a0curl\u00a0of the\u00a0vector field\u00a0to a\u00a0line integral\u00a0of the vector field around the boundary of the surface.<\/span><\/li>\r\n\t
  14. Logic gates, truth tables and simplification of circuits<\/a><\/span><\/li>\r\n\t
  15. Thevenin\u2019s theorem<\/a>: How to analyse circuits using this theorem<\/span><\/li>\r\n\t
  16. Norton\u2019s theorem<\/a>: Exploring Norton\u2019s theorem in simplifying circuits along with laws of Boolean Algebra.<\/span><\/li>\r\n\t
  17. Millman\u2019s theorem and equation<\/a>: Millman\u2019s Theorem is nothing more than a long equation, applied to any circuit drawn as a set of parallel-connected branches, each branch with its own voltage source and series resistance.<\/span><\/li>\r\n\t
  18. Bode diagram<\/a>: Bode diagrams are graphical representations of the frequency responses and are used in solving design problems.<\/span><\/li>\r\n\t
  19. Cayley-Hamilton Theorem<\/a>: Explore the Cayley-Hamilton theorem in reducing the order of a polynomial or to determine analytic functions of a matrix.<\/span><\/li>\r\n\t
  20. Length of a curve on a surface<\/a>: Explore the length of a curve on a surface using Calculus.<\/span><\/li>\r\n<\/ol>","protected":false},"excerpt":{"rendered":"Predicting fire spread in wildlife fields: This mathematical model of fire presented in this paper offers for the first time a method for making quantitative evaluation of both rate of spread and fire intensity in fuels that qualify for the assumptions made on the model.\u00a0 The model didn’t use any prior knowledge of a fuel’s […]","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"amp_status":"","footnotes":""},"class_list":["post-1019","page","type-page","status-publish","hentry","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/pages\/1019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1019"}],"version-history":[{"count":6,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/pages\/1019\/revisions"}],"predecessor-version":[{"id":1229,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/pages\/1019\/revisions\/1229"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}