# Boost C++ Libraries

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## The Mathematical Constants

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

root_three

√3

1.73205

half_root_two

√2 /2

0.707106

ln_two

ln(2)

0.693147

ln_ten

ln(10)

2.30258

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

π and related

pi

pi

3.14159

Ubiquitous. Archimedes constant π

half_pi

π/2

1.570796

third_pi

π/3

1.04719

sixth_pi

π/6

0.523598

two_pi

6.28318

Many uses, most simply, circumference of a circle

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_root_pi

1/√π

0.564189

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

πe

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

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

one_div_log10_e

1/log10(e)

2.30258

Trigonometric

degree

radians = π / 180

0.017453

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

euler2

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)/ 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_kurtosis

3+(6π2-24π+16)/(4-π)2

3.245089

Rayleigh distribution kurtosis

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: `static_cast(42)`.
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.
 Copyright © 2006-2010, 2012-2014, 2017 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)