arsd.gr

Math library providing constants and functions for working with the golden ratio.

φ = \frac{a + b}{a} = \frac{a}{b}

import arsd.gr;

void main() {
	import std.conv;
	import std.string;
	import std.stdio;

	// `arsd.gr.goldenRatio` is a compile-time constant
	// holding the value representing the golden ratio.
	float gr = goldenRatio;
	writeln(i"The golden ratio is $(gr).");

	while (true) {
		// Prompt user to enter a length.
		write("\nEnter combined length: ");
		string rawUserInput = readln().chomp();

		// Parse user input string into a numeric floating-point value.
		float combinedLength;
		try {
			combinedLength = rawUserInput.to!float;
		}
		catch (Exception) {
			// Print error message and continue with another prompt.
			writeln("Bad input.");
			continue;
		}

		// Construct a GoldenRatioLengths structure.
		GoldenRatioLengths!float lengths = goldenRatioLengthsFromAB(combinedLength);

		// Calculate and print lengths.
		writeln(i"AB: $(lengths.ab)");
		writeln(i"a:  $(lengths.a)");
		writeln(i"b:  $(lengths.b)");
	}
}

Command-line calculator app

To build the command-line app for the golden ratio calculator, run one of the following commands.

# Run it directly from your favorite compiler.
dmd     -version=ArsdGrCalculatorMain -run gr.d -- <args>
ldc2 --d-version=ArsdGrCalculatorMain -run gr.d -- <args>

# Using rdmd works, too.
rdmd    -version=ArsdGrCalculatorMain      gr.d -- <args>

# Run it with DUB, either by fetching it from the registry or directly from its folder.
dub run --config=calculator  arsd-official:gr   -- <args>
dub run --config=calculator               :gr   -- <args>

# Or just execute this very file. (POSIX only)
./gr.d  <args>

A short help text with usage instructions can be printed by running the command-line app with argument --help.

In mathematics, the golden ratio — usually denoted by Greek lowercase letter phi φ — is the partitioning ratio of a line segment in two subsegments that share the same ratio to each other as the combined line segment to the longer subsegment.

φ = \frac{a + b}{a} = \frac{a}{b}

Variable declarations
Symbol	Meaning
φ	Golden ratio
AB	A combined line segment whose length is the sum of its two subsegments in the golden ratio.
a	Longer subsegment of the combined line segment `AB` in the golden ratio.
b	Shorter subsegment of combined line segment `AB` in the golden ratio.

The golden ratio can be calculated using the positive solution of following formula:

φ = φ^{2} - 1

φ = \frac{1 + \sqrt{5}}{2} = 1.61803\dots

From this it follows that for a line segment AB the longer subsegment a can be calculated with this formula:

a (\overset{—}{AB}) = \frac{\overset{—}{AB}}{2} (\sqrt{5} - 1) = \overset{—}{AB} \times 0.61803\dots

The shorter subsegment b of a line segment AB is therefore calculated as follows:

b (\overset{—}{AB}) = \frac{\overset{—}{AB}}{2} (3 - \sqrt{5}) = \overset{—}{AB} \times 0.38196\dots

Members

Functions

goldenRatioLengthsFromA GoldenRatioLengths!Float goldenRatioLengthsFromA(Float value): Constructs a GoldenRatioLengths structure from the provided value for a.
goldenRatioLengthsFromAB GoldenRatioLengths!Float goldenRatioLengthsFromAB(Float value): Constructs a GoldenRatioLengths structure from the provided value for AB.
goldenRatioLengthsFromB GoldenRatioLengths!Float goldenRatioLengthsFromB(Float value): Constructs a GoldenRatioLengths structure from the provided value for b.
main int main(string[] args): This is the optional library-provided main() function for the built-in calculator app.
runGoldenRatioCalculatorApp int runGoldenRatioCalculatorApp(string[] args, std.stdio.File stdin, std.stdio.File stdout, std.stdio.File stderr): Portable entrypoint of the command-line calculator app.

Manifest constants

goldenRatio enum goldenRatio;: The golden ratio.

Structs

GoldenRatioLengths struct GoldenRatioLengths(Float): Golden ratio line segment lengths.

arsd modules

Articles

Overviews, concepts, and tutorials