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Mathematics Dictionary
Dr. K. G. Shih
Question and Answer
Questions


  • Keyword | Calculus : Integral Table
  • Keyword | Calculus : Diagrams
  • Keyword | Calculus : Calculus Index
  • Keyword | Calculus : Subjects
  • Keyword | Centroid, Circum-center and orth-center are colinear
  • Keyword | Centroid theory
  • Keyword | Chebyshev's polynomial in Pascal triangle
  • Keyword | Chord : How many chords can be drawn if 11 points on circle ?
  • Keyword | Circle equations in various coordinates
  • Keyword | Circle : Locus
    • 1. Equation of circle
    • 2. Locus of x^2 + y^2 - 6*x + 6*y - 07 = 0
    • 3. Locus of x^2 + y^2 - 6*x + 6*y + 18 = 0
    • 4. Locus of x^2 + y^2 - 6*x + 6*y + 43 = 0
    • 5. Locus of R = sin(A)
    • 6. Locus of R = cos(A)
  • Keyword | Circle : Draw 4 circles to tangent triangle ABC
    • 1. Draw 1 in-circle of triangle ABC
    • 2. Draw 3 ex-cirlce of triangle ABC
  • Keyword | Circum-center, centroid and orth-center are colinear
  • Keyword | Circum-center theory of triangle ABC
    • Side a = 2*R*sin(A)
    • Side b = 2*R*sin(B)
    • Side c = 2*R*sin(C)
  • Keyword | Clock : Angle between two hands
    • 1. Two hands coincide
    • 2. Two hands make 180 degrees angle
  • Keyword | Colinear of 3 points
  • Keyword | Color codes in HTML : ff0000=red 00ff00=green 0000ff=blue
  • Keyword | Completing square method and application.
  • Keyword | Complex numbers
    • z = a + b*i
    • z = cos(A) + i*sin(A)
    • Conjugate of complex number
  • Keyword | Construction geometry
    • 1. Change quadrilateral to equal area triangle
    • 2. Construct an excentral triangle
  • Keyword | Construction : Divide line into 3 equal parts
  • Keyword | Construction : Conic sections
  • Keyword | Construction : Ex-central triangle
  • Keyword | Conic Sections
    • Circle
    • Ellipse
    • Hyperbola
    • Parabola
    • Illiminate x*y term in F(x, y) = 0
  • Keyword | Conic Sections : Sketch of circle of F(x, y) = 0
  • Keyword | Conic Sections : Sketch of ellipse of F(x, y) = 0
    • 1. 2*x^2 + 4*y^2 - 4*x - 8*y - 10 = 0
    • 2. 4*x^2 + 2*y^2 - 8*x - 4*y - 10 = 0
  • Keyword | Conic Sections : Sketch of hyperbola of F(x, y) = 0
    • 1. 2*x^2 - 4*y^2 - 4*x - 8*y - 18 = 0
    • 2. 4*x^2 - 2*y^2 - 8*x - 4*y - 14 = 0
  • Keyword | Conic Sections - Eliminate x*y term method
    • 1. Change x*y = 1 to form (x/a)^2 - (y/b)^2 = 1
    • 2. Find focal length and equation of directrix
  • Keyword | Construction Geometry
    • Keyword | Centroid of triangle : 2/3 rule
    • Keyword | Circum-center of triangle : Circle passing vetices of triangle
    • Keyword | Ex-center of triangle : Circle tangents 3 sides of triangle
    • Keyword | Ex-central triangle : 4 Circles tangent 3 sides of triangle
    • Keyword | In-center of triangle : Circle tangents 3 sides of triangle
    • Keyword | Ortho-center of triangle : Draw pedal triangle
    • Keyword | Trinagle with 3 given heights
    • Keyword | Trinagle with 3 given side
    • Keyword | Triangle with 1 given median and 2 sides
    • Keyword | Triangle with 2 given medians and 1 sides
  • Keyword | Coordinate geometry
  • Keyword | Coordinate geometry : Points A(7,4), B(3,1) and C(0,k)
  • Keyword | Cosine function
    • y = cos(x)
    • R = cos(A)
    • Formula of cos(A/2)
    • proof of cossine law
    • proof of cos(A - B) = cos(A)*cos(B) + sin(A)*sin(B)
  • Keyword | Cosine function : Identities in triangle
    • 1. cos(A) + cos(B) + cos(C) = 1 + 4*sin(A/2)*sin(B/2)*sin(C/2)
    • 2. cos(2*A) + cos(2*B) + cos(2*C) = -1 - 4*cos(A)*cos(B)*cos(C)
    • 3. cos(A)^2 + cos(B)^2 + cos(C)^2 = +1 - 2*cos(A)*cos(B)*cos(C)
  • Keyword | Cosine function : Sketch using five points
  • Keyword | Cosine law
    • 1. Prove that sin(A) = 2*Sqr(s*(s-a)*(s-b)*(s-c))/(b*c)
    • 2. Application : Direction of sum of two vectors
    • 3. Heron formula
  • Keyword | Cos(A - B) = cos(A)*cos(B) - sin(A)*sin(B)
  • Keyword | Cubic functions with 3 zeros : Find expression
    • 1. Method 1 : y = (x - r)*(x - s)*(x - t)
    • 2. Method 2 : Equation thoery
  • Keyword | Cubes in cubes patterns
    • Sketch a cubes in cubes patterns for 5^3


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