Maths Exploration (IA) ideas

  1. 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.  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.
  2. Butterfly network in Computer Algorithm: 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.
  3. Mercator’s Projection: The Mercator projectionis a cylindrical map projectionpresented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course as straight segments that conserve the angles with the meridians.
  4. Catenary Curve: 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 rolling along a straight line. What makes the catenary arch important is its ability to withstand weight. For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve.
  5. Cissoid of Dicoles: Diocles(~250 – ~100 BC) invented this curve to solve the doubling 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 cissoids.
  6. Visual acuity: Comparison of Monoyar chart/Snellen chart/Jaggers chart/ Rosenbaum chart
  7. Affine Transformation: Affine transformationis a linear mapping method that preserves points, straight lines, and planes. Sets of parallel lines remain parallel after an affine transformation.
  8. Liu Hui’s π inequality: Liu Hui proved an inequality involving πby considering the area of inscribed polygons with Nand 2N sides.
  9. Binet’s Formula: Binet’s formula is an explicit formula used to find the  th term of the Fibonacci sequence.
  10. Omar Khayyam’s solution of a cubic equation: 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.
  11. Bernstein Polynomial: Expansions in Bernstein polynomials have a slow rate of convergence. For that reason, following Bernstein’s application to the Weierstrass theorem, these polynomials had little impact in numerical analysis.
  12. Four-color theorem: The four color theoremstates 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.
  13. Stoke’s theorem: Stokes’ theoremrelates a surface integralof a the curl of the vector field to a line integral of the vector field around the boundary of the surface.
  14. Logic gates, truth tables and simplification of circuits
  15. Thevenin’s theorem: How to analyse circuits using this theorem
  16. Norton’s theorem: Exploring Norton’s theorem in simplifying circuits along with laws of Boolean Algebra.
  17. Millman’s theorem and equation: Millman’s 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.
  18. Bode diagram: Bode diagrams are graphical representations of the frequency responses and are used in solving design problems.
  19. Cayley-Hamilton Theorem: Explore the Cayley-Hamilton theorem in reducing the order of a polynomial or to determine analytic functions of a matrix.
  20. Length of a curve on a surface: Explore the length of a curve on a surface using Calculus.