Math::N...angular(3)

✨ Math::N...angular(3) ✨

okay so bestie — this is a page from the User Contributed Perl Documentation collection, and it's all about Math::NumSeq::Triangular, aka triangular numbers 🎀. Buckle up, it's lowkey adorable and highkey useful.

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💖 NAME 💖

Math::NumSeq::Triangular — triangular numbers. That's it, that's the vibe 🦋

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🌸 SYNOPSIS 🌸

use Math::NumSeq::Triangular;
my $seq = Math::NumSeq::Triangular->new;
my ($i, $value) = $seq->next;

three lines and you're in, no cap 💅

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🦋 DESCRIPTION 🦋

So the triangular numbers are literally i*(i+1)/2, and they go like:

0, 1, 3, 6, 10, 15, 21, 28, ...
starting i=0

The way that these numbers are just how many points fit in an equilateral triangle of side i?? Obsessed. Look:

   *      i=1  1

   *      i=2  3
  * *

   *
  * *     i=3  6
 * * *

   *
  * *     i=4  10
 * * *
* * * *

fr fr, it's giving geometry and I ate 🍓

And here's the cute part: from a given i, the next value is formed by adding i+1 — that's a new row of that length plopped on the bottom of the triangle. Stacking rows like a little pointy staircase 👑✨

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💜 FUNCTIONS 💜

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes. (iykyk — that's the family, go say hi 🫶)

• "$seq = Math::NumSeq::Triangular->new ()" — creates and returns a brand new sequence object. main character energy, honestly 💅

🔥 Random Access 🔥

• "$value = $seq->ith($i)" — hands you back "$i*($i+1)/2". yes that exact thing. no notes.
• "$bool = $seq->pred($value)" — returns true if $value is a triangular number, meaning it's i*(i+1)/2 for some integer i. vibe check passed ✅
• "$i = $seq->value_to_i_ceil($value)"
• "$i = $seq->value_to_i_floor($value)" — returns the index i of $value. but if $value is NOT a triangular number, then you get the next higher index for "ceil" or the next lower one for "floor". it rounds, bestie, it's just doing its best 🥺
• "$i = $seq->value_to_i_estimate($value)" — returns an estimate of the i that corresponds to $value. it takes value=i*(i+1)/2 and inverts it into:

$i = int ((sqrt(8*$value + 1) - 1)/2)

MATH! ✨ MATH! ✨ MATH! we love a formula that knows its own inverse 😭💖

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👑 SEE ALSO 👑

• Math::NumSeq
• Math::NumSeq::Pronic
• Math::NumSeq::Squares

the whole friend group, go check them out 🌈

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🌈 HOME PAGE 🌈

<http://user42.tuxfamily.org/math-numseq/index.html>

click it, bestie, it's where the lore lives 🦋

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🎀 LICENSE 🎀

Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.

yes the ALL CAPS warranty disclaimer is staying, it's literally the law of the land, do not touch it 💀

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and that's the whole page, bestie!! 🫶 this one came from perl v5.42.0, dated 2025-07-25, and it's filed under Math::N...angular(3). slay, go forth and triangulate 💖✨🌸🎀🦋💅