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Math::Angle - a class to handle geometric angles


use Math::Angle;
my= Math::Angle.new(deg => 63.4);
say φ.sin;
say cos φ;


Math::Angle defines objects which represent angles. It was written to try to prevent the problems I kept encountering in forgetting to convert angles between radians and degrees.

Thus an angle may be defined in terms of radians, degrees or grads, and then used in trigonometric expressions without concern for conversion between units.

The standard trigonometric functions available in Raku can all be used as either methods on the Math::Angle object, or as functions with the Math::Angle object as argument.

In addition, subroutines are available for the inverse trigonometric functions which return a Math::Angle object.

Some basic arithmetic using Math::Angle objects is also possible where it makes sense.

Object creation

Math::Angle objects are created by calling the Math::Angle.new routine with a named argument specifying the angle required. The following three possibilities are equivalent:

my $φ = Math::Angle.new(rad => π/4);
my $η = Math::Angle.new(deg => 45);
my $θ = Math::Angle.new(grad => 50);

Accessing the angle value

The angle embedded within a Math::Angle object can be accessed using the three methods rad, deg, and grad which convert the internal value to the requested representation

Note that it is thus possible to convert an angle from degrees to radians by writing

Math::Angle.new(deg => 27).rad


Arithmetic involving Math::Angle objects is possible where it makes sense:

my1 = Math::Angle.new(:37deg);
my2 = Math::Angle.new(rad => π/6);
say (φ1 - φ2).deg;
say (φ1 + φ2).rad;
say (φ1 × 2).rad;
say (4 × φ2).deg;
say φ1 ÷ φ2;

With the exception of division, the results of all those objects will be a Math::Angle object. The result of the division is a plain number representing the ratio of the two angles.


Math::Angle has two coercion methods, Numeric and Comples. Numeric returns the numeric value of the angle in radians. Complex returns a complex number with radius 1 and angle given by the Math::Angle object.

Math::Angle also inherits from Cool. When combined with the Numeric coercion, this gives access to the trigonometric functions sin, cos, tan, sec, cosec, cotan, sinh, cosh, tanh, sech. cosech, and cotanh. These may all be used as functions with the Math::Angle object as argument, or as methods on the Math::Angle object.

It probably also leads to all sorts of other undesirable effects.


The following standard trigonometric functions may be used to return a Math::Angle object: asin, acos, atan, atan2, asec, acosec, acotan, asinh, acosh, atanh, asech, acosech, and acotanh.


from-dms takes a string argument representing an angle in degrees, minutes and seconds, and converts it into a Math::Angle object.

The string contains:

The various fields may be separated by white space.

The decimal numbers can be fractional, and contain exponents such as 12.53e5.

Note that no sanity checks are made. An angle of "-2473.2857° 372974.2746′ 17382.2948e5s W" is acceptable, and equal to about 491531.046°. The values for degrees, minutes and seconds are simply added together with the appropriate scaling and with the appropriate sign calculated from the initial sign and the hemisphere.

If the seconds are designated by the letter S and a hemisphere is also specified, then they must be separated by whitespace.

Alternative representations

Two methods are available to produce string output in useful forms for angles expressed in degrees.


Method dms will return a string containing a representation of the angle in degrees, minutes and seconds. For example:

Math::Angle.new(rad => 0.82).dms.say; # 46° 58′ 57.1411″

However the output is fairly configurable. For example, signed numbers can be output in various forms:

Math::Angle.new(rad => -0.82).dms.say; # -46° 58′ 57.1411″
Math::Angle.new(rad => 0.82).dms(presign=>"+-").say; # +46° 58′ 57.1411″
Math::Angle.new(rad => 0.82).dms(presign=>"", postsign=>"NS").say; # 46° 58′ 57.1411″N
Math::Angle.new(rad => -0.82).dms(presign=>"", postsign=>"NS").say; # 46° 58′ 57.1411″S
Math::Angle.new(rad => -0.82).dms(presign=>"", postsign=>"EW").say; # 46° 58′ 57.1411″W

The full set of options is:

degsymA string representing the symbol printed after the number of degrees"°" (unicode U00B0 — DEGREE SIGN)
minsymA string representing the symbol printed after the number of minutes"′" (unicode U2032 — PRIME)
secsym(dms only) A string giving the symbol printed after the number of seconds'″' (unicode U2033 — DOUBLE PRIME)
presignA string where the first chracter is printed before a positive number, and the second character is printed before a negative number" -" (a space and a minus sign)
postsignA string where the first character is printed after a positive number, and the second character is printed after a negative number" " (two spaces)
separatorA string printed between the degrees and minutes, and between the minutes and seconds" "
secfmt(dms only) The format string for the seconds field"%.4f"
minfmt(dm only) The format string for the minutes field"%.4f"

Note for presign and postsign that a blank in the string is not printed.


Method dm will return a string containing a representation of the angle in degrees and minutes. For example:

Math::Angle.new(rad => 0.82).dm.say; # 46° 58' 57.1411"

The same configurability as in dms is available:

Math::Angle.new(rad => -0.82).dm.say; # -46° 58.9524′
Math::Angle.new(rad => 0.82).dm(presign=>"+-").say; # +46° 58.9524′
Math::Angle.new(rad => 0.82).dm(presign=>"", postsign=>"NS").say; # 46° 58.9524'N
Math::Angle.new(rad => -0.82).dm(presign=>"", postsign=>"NS").say; # 46° 58.9524′S
Math::Angle.new(rad => -0.82).dm(presign=>"", postsign=>"EW").say; # 46° 58.9524′W

The options are the same as for dms, except that secsig is not available and secfmt is replaced by minfmt.


Kevin Pye kjpraku@pye.id.au


Copyright 2022 Kevin Pye

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.