Rational fractions

half

1/2

0.5

third

1/3

0.333333

two_thirds

2/3

0.66667

three_quarters

3/4

0.75

two and related

root_two

√2

1.41421

Equivalent to POSIX constant M_SQRT2

root_three

√3

1.73205

half_root_two

√2 /2

0.707106

ln_two

ln(2)

0.693147

Equivalent to POSIX constant M_LN2

ln_ten

ln(10)

2.30258

Equivalent to POSIX constant M_LN10

ln_ln_two

ln(ln(2))

-0.366512

Gumbel distribution median

root_ln_four

√ln(4)

1.177410

one_div_root_two

1/√2

0.707106

Equivalent to POSIX constant M_SQRT1_2

π and related

pi

π

3.14159

Ubiquitous. Archimedes constant π. Equivalent to POSIX constant M_PI

half_pi

π/2

1.570796

Equivalent to POSIX constant M_PI2

third_pi

π/3

1.04719

quarter_pi

π/4

0.78539816

Equivalent to POSIX constant M_PI_4

sixth_pi

π/6

0.523598

two_pi

2π

6.28318

Many uses, most simply, circumference of a circle

tau

τ

6.28318

@https://en.wikipedia.org/wiki/Turn_(angle)#Tau_proposals Many uses, most simply, circumference of a circle. Equal to two_pi.

two_thirds_pi

2/3 π

2.09439

volume of a hemi-sphere = 4/3 π r³

three_quarters_pi

3/4 π

2.35619

= 3/4 π

four_thirds_pi

4/3 π

4.18879

volume of a sphere = 4/3 π r³

one_div_two_pi

1/(2π)

1.59155

Widely used

root_pi

√π

1.77245

Widely used

root_half_pi

√ π/2

1.25331

Widely used

root_two_pi

√ π*2

2.50662

Widely used

one_div_pi

1/π

0.31830988

Equivalent to POSIX constant M_1_PI

two_div_pi

2/π

0.63661977

Equivalent to POSIX constant M_2_PI

one_div_root_pi

1/√π

0.564189

two_div_root_pi

2/√π

1.128379

Equivalent to POSIX constant M_2_SQRTPI

one_div_root_two_pi

1/√(2π)

0.398942

root_one_div_pi

√(1/π

0.564189

pi_minus_three

π-3

0.141593

four_minus_pi

4 -π

0.858407

pi_pow_e

π^e

22.4591

pi_sqr

π²

9.86960

pi_sqr_div_six

π²/6

1.64493

pi_cubed

π³

31.00627

cbrt_pi

√³ π

1.46459

one_div_cbrt_pi

1/√³ π

0.682784

Euler's e and related

e

e

2.71828

Euler's constant e, equivalent to POSIX constant M_E

exp_minus_half

e ^-1/2

0.606530

e_pow_pi

e ^π

23.14069

root_e

√ e

1.64872

log10_e

log10(e)

0.434294

Equivalent to POSIX constant M_LOG10E

one_div_log10_e

1/log10(e)

2.30258

log2_e

log₂(e)

1.442695

This is the same as 1/ln(2) and is equivalent to POSIX constant M_LOG2E

Trigonometric

degree

radians = π / 180

0.017453

radian

degrees = 180 / π

57.2957

sin_one

sin(1)

0.841470

cos_one

cos(1)

0.54030

sinh_one

sinh(1)

1.17520

cosh_one

cosh(1)

1.54308

Phi

Phidias golden ratio

Phidias golden ratio

phi

(1 + √5) /2

1.61803

finance

ln_phi

ln(φ)

0.48121

one_div_ln_phi

1/ln(φ)

2.07808

Euler's Gamma

euler

euler

0.577215

Euler-Mascheroni gamma constant

one_div_euler

1/euler

1.73245

euler_sqr

euler²

0.333177

Misc

zeta_two

ζ(2)

1.64493

Riemann zeta function

zeta_three

ζ(3)

1.20205

Riemann zeta function

catalan

K

0.915965

Catalan (or Glaisher) combinatorial constant

glaisher

A

1.28242

Decimal expansion of Glaisher-Kinkelin constant

khinchin

k

2.685452

Decimal expansion of Khinchin constant

extreme_value_skewness

12√6 ζ(3)/ π³

1.139547

Extreme value distribution

rayleigh_skewness

2√π(π-3)/(4 - π)^3/2

0.631110

Rayleigh distribution skewness

rayleigh_kurtosis_excess

-(6π²-24π+16)/(4-π)²

0.245089

Rayleigh distribution kurtosis excess

rayleigh_kurtosis

3+(6π²-24π+16)/(4-π)²

3.245089

Rayleigh distribution kurtosis

first_feigenbaum

4.6692016

First Feigenbaum constant

plastic

Real solution of x³ = x + 1

1.324717957

Plastic constant

gauss

Reciprocal of agm(1, √2)

0.8346268

Gauss's constant

dottie

Solution of cos(x) = x

0.739085

Dottie's number

reciprocal_fibonacci

Sum of reciprocals of Fibonacci numbers

3.359885666

Reciprocal Fibonacci constant

laplace_limit

.6627434193

Laplace Limit