From a881f7518d1c02092c6f8700222ebf129f2a650c Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Sat, 19 Apr 2025 20:42:09 -0400
Subject: [PATCH] use a sage function for polygonal numbers

---
 notebooks/problem0012.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/notebooks/problem0012.ipynb b/notebooks/problem0012.ipynb
index 970f9eb..e3c0055 100644
--- a/notebooks/problem0012.ipynb
+++ b/notebooks/problem0012.ipynb
@@ -7,7 +7,7 @@
    "source": [
     "# [Highly Divisible Triangular Number](https://projecteuler.net/problem=12)\n",
     "\n",
-    "Yet another problem with a straightforward solution thanks to SageMath's preinstalled functions. We'll also once again apply the closed formula for triangle numbers (see [problem 1](https://projecteuler.net/problem=1))."
+    "Yet another problem with a straightforward solution thanks to SageMath's preinstalled functions. Triangular numbers fall into the broader category of [polygonal numbers](https://en.wikipedia.org/wiki/Polygonal_number)."
    ]
   },
   {
@@ -26,7 +26,7 @@
    ],
    "source": [
     "for n in PositiveIntegers():\n",
-    "    t = n * (n+1) / 2\n",
+    "    t = polygonal_number(3, n)\n",
     "    if number_of_divisors(t) > 500:\n",
     "        print(t)\n",
     "        break"