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Mathematical Constants, Squares, Cubes & Roots

150 cards · 🇺🇸 English

Pi, e, the golden ratio, plus perfect squares, cubes and square roots.

general-mathconstantssquaresroots

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Mathematical constant

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  1. 1Mathematical constant
    A number whose value is fixed by an unambiguous definition, often referred to by a special symbol
  2. 2Π (pi)
    The ratio between the circumference and diameter of a circle
  3. 3Approximate value of π
    3.14159265358979...
  4. 4Is π rational or irrational?
    Irrational (and transcendental)
  5. 5Good rational approximation of π
    22/7 or 355/113 (more accurate)
  6. 6E (Euler's number)
    The base of natural logarithms, lim(n→∞)(1 + 1/n)ⁿ
  7. 7Approximate value of e
    2.71828182845904...
  8. 8Is e rational or irrational?
    Irrational and transcendental
  9. 9Imaginary unit i
    The number defined by i² = -1
  10. 10Why is the imaginary unit called 'imaginary'?
    Because there is no real number whose square is negative
  11. 11What symbol is sometimes used instead of i in electrical engineering?
    j (because i is used for electric current)
  12. 12Φ (phi), the golden ratio
    The ratio (1 + √5)/2, approximately 1.618...
  13. 13Approximate value of φ
    1.61803398874989...
  14. 14Relationship between φ and Fibonacci numbers
    φ is the limit of the ratio of consecutive Fibonacci numbers
  15. 15√2 also
    Pythagoras' constant
  16. 16Approximate value of √2
    1.41421356237309...
  17. 17Is √2 rational or irrational?
    Irrational (but algebraic)
  18. 18Quick approximation for √2
    99/70 ≈ 1.41429 (differs by less than 1/10,000)
  19. 19Γ (gamma), the Euler-Mascheroni constant
    The limiting difference between the harmonic series and the natural logarithm: lim(n→∞)[Σ(1/k) - ln(n)]
  20. 20Approximate value of γ
    0.57721566490153...
  21. 21Is the Euler-Mascheroni constant rational or irrational?
    Unknown (it is an open question)
  22. 22Apéry's constant
    ζ(3) = Σ(n=1 to ∞) 1/n³
  23. 23Approximate value of Apéry's constant
    1.20205690315959...
  24. 24Catalan's constant G
    The alternating sum: Σ(n=0 to ∞) (-1)ⁿ/(2n+1)²
  25. 25Approximate value of Catalan's constant
    0.91596559417721...
  26. 26Is Catalan's constant known to be irrational?
    No, it is unknown (strongly suspected but unproven)
  27. 27Feigenbaum constants
    Mathematical invariants (δ and α) of logistic maps in chaos theory
  28. 28Approximate value of the Feigenbaum delta (δ)
    4.66920160910299...
  29. 29Approximate value of the Feigenbaum alpha (α)
    2.50290787509589...
  30. 30√3 also
    Theodorus' constant

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