Figural

A tiny library for generating, evaluating, and plotting triangular and pentagonal numbers in Python.

Installation

You can install figural using PyPI:

pip install figural

Or from source. Here I am using uv but you can use any Python environment of your choice:

git clone https://github.com/twaclaw/figural.git
cd figural
uv venv --python=3.14
source ./venv/bin/activate
uv pip install -e .

Examples

Generating the ith numbers and testing for membership

import figural.triangular as tr
import figural.pentagonal as pn

tr.ith(5)
# 15

pn.ith(5)
# 35

tr.is_triangular(15)
# np.True_

pn.is_pentagonal(pn.ith(10000000))
# np.True_

Generating ranges

import figural.triangular as tr
import figural.pentagonal as pn
import numpy as np

tr.arange(10)
# array([ 1,  3,  6, 10, 15, 21, 28, 36, 45])

pn.arange(10)
# array([  1,   5,  12,  22,  35,  51,  70,  92, 117, 145])

np.all(pn.is_pentagonal(pn.arange(int(1e8))))
# np.True_

Plotting individual numbers

tr.draw_ith(5, with_label=True)

tr.draw_ith(5, with_label=True, color="red", marker_style="^", draw_contourn=False)

pn.draw_ith(5, with_label=True, color="green")

tr.draw_ith(3, with_label=True, return_tikz=True)

Click to expand TikZ code

% This file was created with tikzplotlib v0.10.1.
\begin{tikzpicture}

\definecolor{darkgrey176}{RGB}{176,176,176}

\begin{axis}[
hide x axis,
hide y axis,
tick align=outside,
tick pos=left,
x grid style={darkgrey176},
xmin=-0.05, xmax=1.05,
xtick style={color=black},
y grid style={darkgrey176},
ymin=-0.05, ymax=1.05,
ytick style={color=black}
]
\addplot [black]
table {%
0 0
1 0
0.5 1
0 0
};
\addplot [semithick, black, mark=*, mark size=5, mark options={solid}, only marks]
table {%
0 0
0.5 0
1 0
};
\addplot [semithick, black, mark=*, mark size=5, mark options={solid}, only marks]
table {%
0.25 0.5
0.75 0.5
};
\addplot [semithick, black, mark=*, mark size=5, mark options={solid}, only marks]
table {%
0.5 1
};
\draw (axis cs:0.5,-0.25) node[
    scale=0.6,
    anchor=north,
    text=black,
    rotate=0.0
]{$T_{3}=6$};
\end{axis}

\end{tikzpicture}

Plotting ranges of numbers

tr.draw_range(1, 6, with_label=True, cols=3, draw_grid=True)

pn.draw_range(1, 8, with_label=True, cols=4, draw_grid=True, color='blue')

Contributing

Sure thing! Feel fre to open an issue or create a pull request.