...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
This section lists the mathematical constants, their use(s) (and sometimes rationale for their inclusion).
Table 4.1. Mathematical Constants
name 
formula 
Value (6 decimals) 
Uses and Rationale 

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 hemisphere = 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 
π3 
0.141593 

four_minus_pi 
4 π 
0.858407 

pi_pow_e 
π^{e} 
22.4591 

pi_sqr 
π^{2} 
9.86960 

pi_sqr_div_six 
π^{2}/6 
1.64493 

pi_cubed 
π^{3} 
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 
log_{2}(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 

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 

one_div_euler 
1/euler 
1.73245 

euler_sqr 
euler^{2} 
0.333177 

Misc 

zeta_two 
ζ(2) 
1.64493 

zeta_three 
ζ(3) 
1.20205 

catalan 
K 
0.915965 

glaisher 
A 
1.28242 

khinchin 
k 
2.685452 

extreme_value_skewness 
12√6 ζ(3)/ π^{3} 
1.139547 
Extreme value distribution 
rayleigh_skewness 
2√π(π3)/(4  π)^{3/2} 
0.631110 
Rayleigh distribution skewness 
rayleigh_kurtosis_excess 
(6π^{2}24π+16)/(4π)^{2} 
0.245089 

rayleigh_kurtosis 
3+(6π^{2}24π+16)/(4π)^{2} 
3.245089 
Rayleigh distribution kurtosis 
first_feigenbaum 
4.6692016 

plastic 
Real solution of x^{3} = x + 1 
1.324717957 

gauss 
Reciprocal of agm(1, √2) 
0.8346268 

dottie 
Solution of cos(x) = x 
0.739085 

reciprocal_fibonacci 
Sum of reciprocals of Fibonacci numbers 
3.359885666 

laplace_limit 
.6627434193 
Note  

Integer values are not included in this
list of math constants, however interesting, because they can be so easily
and exactly constructed, even for UDT, for example: 
Tip  

If you know the approximate value of the constant, you can search for the value to find Boost.Math chosen name in this table. 
Tip  

Bernoulli numbers are available at Bernoulli numbers. 
Tip  

Factorials are available at factorial. 