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



  • Keyword | Parabola : Defintion and Equations
  • Keyword | Parabola : Locus y = (x^2)/(2*D) - D/2
  • Keyword | Parabola : Sketch
    • Convert R = D/(1 - sin(A)) to rectangular form
  • Keyword | Parabola : Polar form
    • 1. Compare R = D/(1 - sin(A)) with R = D/(1 - cos(A))
    • 2. Compare R = D/(1 - sin(A)) with y = (x^2)/(2*D) - D/2
    • 3. Compare R = D/(1 - sin(A)) with y = a*(x^2) + B*x + c
  • Keyword | Parabola : Quadratic function
    • 1. Properties of y = a*x^2 + b*x + c
    • 2. Parabola of y = a*x^2 + b*x + c
  • Keyword | Parabola : Sketch using ruler
  • Keyword | Parabola : Sketch tangent using reflection
  • Keyword | Parametric equations
    • 1. Describe the graph of x = sec(t) and y = tan(t)
    • 2. Describe the graph of x = tan(t) and y = sec(t)
  • Keyword | Parametric equations
    • 1. Skethc the graph of x = t^3 - 3*t and y = t^2 + 1
    • 2. Find angle at intersection of the curve
  • Keyword | Parametric equation : x = sec(t) and y = tan(t)
    • 1. Find coordinate of foci
    • 2. Find equation of asymptotes
  • Keyword | Partial Fractions
  • Keyword | Pascal triangle and Chebyshev's polynomial
  • Keyword | Pascal triangle and polynomial expansion terms
    • 1. Expansion terms of (a + b + c)^n = (n + 1)*(n + 2)/(2!)
    • 2. Expansion terms of (a + b + c + d)^n = (n + 1)*(n + 2)*(n + 3)/(3!)
  • Keyword | Pascal triangle and Fibonacci's sequence
  • Keyword | Pascal triangle and Fibonacci's sequence
    • T(0) = 0 and T(1) = 1
    • T(k+2) = T(k) + T(k+1)
  • Keyword | Pascal triangle and sequences
    • Prove that Sum[C(n+1,2)] = C(n+2,3)
    • Prove that Sum[C(n+2,3)] = C(n+3,4)
    • Prove that Sum[C(n+3,4)] = C(n+4,5)
  • Keyword | Pascal triangle and sequences
    • Prove that Sum[n*(n+1)/2] = n*(n+1)*(n+2)/(3!)
    • Prove that Sum[n*(n+1)*(n+2)/(3!)] = n*(n+1)*(n+2)*(n+3)/(4!)
    • Prove that Sum[n*(n+1)*(n+2)*(n+3)/(4!)] = n*(n+1)*(n+2)*(n+3)*(n+4)/(5!)
  • Keyword | Pascal triangle and series
    • Sum[n] = n*(n+1)/2 = C(n+1,2)
    • Sum[n*(n+1)/2] = n*(n+1)*(n+2)/3! = C(n+2,3)
  • Keyword | Pascal triangle and series
    • Sum[C(n+1),2] = C(n+2,3)
    • Sum[C(n+2),3] = C(n+3,4)
    • Sum[C(n+3),4] = C(n+4,5)
  • Keyword | Pascal triangle and symmetrical matrix order 5
    • 1. Find element row 1 and column 5 for power 3 of the matrix
    • 2. Find element row 1 and column 5 for power 4 of the matrix
    • 3. Find element row 1 and column 5 for power 5 of the matrix
  • Keyword | Pascal triangle : Pentatope number sequences
  • Keyword | Pascal triangle : Tetrahedral number sequence
  • Keyword | Pascal triangle : Triangular number sequences
  • Keyword | Pattern : Graph of R=1 + 1*sin(9*A/4)^3
  • Keyword | Pattern Mathemtics
  • Keyword | Pedal triangle : Defintion and examples
  • Keyword | Pentagon
    • Change pentagon to an equal area triangle
  • Keyword | Pentatope number sequences in Pascal triangle
  • Keyword | Perfect numbers : Defintion and examples
    • 1. Use the properties of perfect number to find 3rd perfect number
    • 2. Use the properties of perfect number to find 4th perfect number
  • Keyword | Permutation P(n, r) or n^r
  • Keyword | Petals of R = sin(p*A)
    • 1. Prove that graph of R = sin(A) is a circle
    • 2. Prove that graph of R = sin(p*A) has p petals if p is odd
    • 3. Prove that graph of R = sin(p*A) has 2*p petals if p is even
  • Keyword | Petals of R = sin(p*A/2)
    • 1. Prove that graph of R = sin(p*A/2) has 2*p petals if p is odd
    • 2. Prove that graph of R = cos(p*A/2) has 2*p petals if p is odd
    • 3. Twin patterns of R = sin(p*A/2) and R = cos(p*A/2) if p is odd
  • Keyword | Petals of R = sin(p*A/q) : p/q rule
  • Keyword | Pi = 3.14159....
    • 1. Value of pi to 1000 decimal place
    • 2. Story of pi
    • 3. Series of pi
  • Keyword | Pi = 3.14159....
  • Keyword | Point in mathematics
  • Keyword | Polynomial coefficients
    • 1. How many terms in expansion of (x + y + z)^5 ?
    • 2. How many terms in expansion of (x + y + z)^m ?
  • Keyword | Polynomials
  • Keyword | Polynomials by Chebyshev
  • Keyword | Prime numbers
    • 1. All integers can be expressed as product of prime numbers
    • 2. Pattern of prime number
  • Keyword | Probability
    • Three pairs color balls. Put each 2 balls into 3 boxes
    • Find probability all boxes having different color
  • Keyword | Probability
    • Hypergeommetric
    • Find probability with 4 aces for 5 cards
  • Keyword | Probability
    • Hypergeommetric : Find probability
    • 24 electric bulbs with 12.5% defective. Take 3 bulbs and all good
  • Keyword | Properties of quadrilaterals
    • Compare rhombus with square
    • Describe properties of quadrilateral
  • Keyword | Pythagorean Law
    • 1. Pythagorean relations
    • 2. Pythagorean triples


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