Numerical Constants

Overview

Engineering reference data for Numerical Constants in mathematics.

Key Formulas

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Roots of ax² + bx + c = 0.

Pythagorean Theorem

$c^2 = a^2 + b^2$

Right triangle relationship.

Circle Area

$A = \pi r^2$

Area of a circle.

Logarithm

$\log_b(x) = \frac{\ln(x)}{\ln(b)}$

Change of base formula.

Variables

Additional Logarithmic & Radical Constants

The following constants complete the set of fundamental logarithmic and radical values referenced in engineering calculations:

$$2^{1/3} = 1.25992\ 10498\ 94873\ 16476\ 72106\ 07278\ 22836\ 05702\ 51464 \quad (6)$$ $$3^{1/3} = 1.44224\ 95703\ 07408\ 38232\ 16383\ 10780\ 10958\ 83918\ 69253 \quad (7)$$ $$\log_{10}(3) = 0.47712\ 12547\ 19662\ 43729\ 50279\ 03255\ 11530\ 92001\ 28864 \quad (8)$$

These values are derived from the definitions of radical and logarithmic functions. The cube root ($x^{1/3}$) is the inverse operation of cubing a number, while $\log_{10}$ is the base-10 logarithm, crucial for orders of magnitude and decibel calculations in signal processing and acoustics.

References

• Original Source