Naimolihttps://naimoli.com/https://naimoli.com/peter/posts/altshiller-court-solutions-ch2/https://naimoli.com/peter/posts/altshiller-court-solutions-ch2/Solutions to exercises from Chapter 2 of Nathan Altshiller-Court's College GeometryMon, 16 Feb 2026 03:00:00 GMThttps://naimoli.com/peter/posts/algebra-sqrt-problems/https://naimoli.com/peter/posts/algebra-sqrt-problems/Master radical equations through 47+ competition problems from AMC, HMMT, BmMT, and MAΘ. Learn nested radicals, isolation, denesting, and advanced techniques.Thu, 11 Sep 2025 16:37:26 GMThttps://naimoli.com/peter/posts/2xlearning/https://naimoli.com/peter/posts/2xlearning/A statistical analysis of Alpha School's '2x Learning' claim, examining MAP test methodology and why comparing scores across different test bands is misleading.Tue, 01 Jul 2025 07:15:49 GMThttps://naimoli.com/peter/posts/cemc-2025-gauss8-23/https://naimoli.com/peter/posts/cemc-2025-gauss8-23/Solving CEMC 2025 Gauss 8 Problem 23 using modular arithmetic, divisibility rules, and cryptarithmetic. Multiple solutions for contest conditions.Tue, 20 May 2025 01:58:33 GMThttps://naimoli.com/peter/posts/burnside-lemma/https://naimoli.com/peter/posts/burnside-lemma/Learn Burnside's Lemma through intuitive examples and AMC problem solutions. Master counting with symmetries using bracelets, necklaces, and rotations.Wed, 13 Aug 2025 20:09:20 GMThttps://naimoli.com/peter/posts/altshiller-court-solutions/https://naimoli.com/peter/posts/altshiller-court-solutions/Complete solutions and discussions of exercises from Nathan Altshiller-Court's classic text College Geometry: An Introduction to the Modern Geometry of the Triangle and the CircleMon, 16 Feb 2026 03:00:00 GMThttps://naimoli.com/peter/posts/challenging-geo-4-36/https://naimoli.com/peter/posts/challenging-geo-4-36/Solve Posamentier & Salkind's cyclic quadrilateral problem using angle chasing, tangent circles, inscribed angles, and the tangent-chord theoremWed, 31 Dec 2025 04:24:50 GMThttps://naimoli.com/peter/posts/euclidea-shenanigans/https://naimoli.com/peter/posts/euclidea-shenanigans/Critiquing Euclidea Wiki explanations and showing a simpler proof for the 45° angle construction using angle chasing and isosceles triangle properties.Sat, 10 Jan 2026 03:33:28 GMThttps://naimoli.com/peter/posts/jhmt-2011-geometry-6/https://naimoli.com/peter/posts/jhmt-2011-geometry-6/Three approaches to an equilateral triangle problem from JHMT 2011: Law of Cosines, coordinate bash with complex numbers, and an elegant rotation trick.Fri, 09 May 2025 10:06:11 GMThttps://naimoli.com/peter/posts/inscribing-square-in-triangle/https://naimoli.com/peter/posts/inscribing-square-in-triangle/Construct squares inscribed in triangles using homothety and harmonic mean. Features solutions to NYCIML, MathCounts, JHMT, AHSME, and Tournament of Towns problems.Mon, 12 Jan 2026 17:27:59 GMThttps://naimoli.com/peter/posts/jhmt-2018-geometry-10/https://naimoli.com/peter/posts/jhmt-2018-geometry-10/Solve JHMT 2018 Geometry Problem 10 using orthic triangles, the FAST Lemma, altitudes, and similar triangles. Includes complete solution and diagrams.Fri, 13 Jun 2025 06:08:16 GMThttps://naimoli.com/peter/posts/goodtricksbadtricks/https://naimoli.com/peter/posts/goodtricksbadtricks/Exploring good vs bad problem-solving tricks in math competitions through rotation techniques, ratio scaling, and system of equations alternatives.Sat, 28 Jun 2025 02:18:07 GMThttps://naimoli.com/peter/posts/jhmt-2021-geometry-6/https://naimoli.com/peter/posts/jhmt-2021-geometry-6/Solution to JHMT 2021 Geometry #6 using geometric construction. Features angle bisector, equilateral triangles, and SAS congruence in a quadrilateral.Tue, 20 May 2025 14:01:10 GMThttps://naimoli.com/peter/posts/newtons-little-theorem/https://naimoli.com/peter/posts/newtons-little-theorem/Solving MATHCOUNTS counting problems using Newton's Little Formula and finite differences. When is this technique actually useful?Wed, 09 Jul 2025 10:01:39 GMThttps://naimoli.com/peter/posts/power-of-a-point-problems/https://naimoli.com/peter/posts/power-of-a-point-problems/Collection of 50+ Power of a Point problems from AMC, AIME, ARML, BMT, and other math competitions with detailed solutions and synthetic geometry techniques.Sun, 12 Oct 2025 05:00:00 GMThttps://naimoli.com/peter/posts/maths-warrior/https://naimoli.com/peter/posts/maths-warrior/Monte Carlo analysis reveals 79% first-player advantage in SIMOC's dice game. Python simulation uncovers broken mechanics and optimal strategy.Thu, 03 Jul 2025 11:06:24 GMThttps://naimoli.com/peter/posts/euclidea-chord-trisection/https://naimoli.com/peter/posts/euclidea-chord-trisection/Step-by-step proof of Euclidea's chord trisection puzzle using compass and straightedge. Includes optimal 4E solution and AlphaGeometry validation.Thu, 25 Dec 2025 04:25:53 GMThttps://naimoli.com/peter/posts/playing-with-alphageometry/https://naimoli.com/peter/posts/playing-with-alphageometry/Using Google DeepMind's AlphaGeometry AI to prove Euclidea geometry puzzle solutions with geometric mean constructions and homothetyThu, 08 Jan 2026 05:06:20 GMT