<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en"><generator uri="https://jekyllrb.com/" version="4.4.1">Jekyll</generator><link href="https://keivan-mirzaei.com/feed.xml" rel="self" type="application/atom+xml" /><link href="https://keivan-mirzaei.com/" rel="alternate" type="text/html" hreflang="en" /><updated>2026-09-30T14:22:34-06:00</updated><id>https://keivan-mirzaei.com/feed.xml</id><title type="html">Keivan Mirzaei</title><subtitle>Mathematical problems, explorations, interactive learning, and research by Keivan Mirzaei.</subtitle><author><name>Keivan Mirzaei</name></author><entry><title type="html">A three-variable inequality</title><link href="https://keivan-mirzaei.com/notes/a-three-variable-inequality/" rel="alternate" type="text/html" title="A three-variable inequality" /><published>2026-09-30T00:00:00-06:00</published><updated>2026-09-30T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/a-three-variable-inequality</id><author><name>Keivan Mirzaei</name></author><category term="algebra" /><category term="inequalities" /><summary type="html"><![CDATA[Prove a symmetric inequality for arbitrary real x, y, and z.]]></summary></entry><entry><title type="html">The average distance across a circle</title><link href="https://keivan-mirzaei.com/notes/expected-distance-on-a-circle/" rel="alternate" type="text/html" title="The average distance across a circle" /><published>2026-09-30T00:00:00-06:00</published><updated>2026-09-30T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/expected-distance-on-a-circle</id><author><name>Keivan Mirzaei</name></author><category term="probability" /><category term="geometry" /><category term="expectation" /><summary type="html"><![CDATA[Choose two points uniformly on a unit circle. What is their expected straight-line distance?]]></summary></entry><entry><title type="html">Finding an invisible spaceship</title><link href="https://keivan-mirzaei.com/notes/finding-an-invisible-spaceship/" rel="alternate" type="text/html" title="Finding an invisible spaceship" /><published>2026-09-30T00:00:00-06:00</published><updated>2026-09-30T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/finding-an-invisible-spaceship</id><author><name>Keivan Mirzaei</name></author><category term="combinatorics" /><category term="puzzles" /><summary type="html"><![CDATA[Can a fixed collection of detectors distinguish every possible 2 × 2 spaceship position on a 7 × 7 board?]]></summary></entry><entry><title type="html">Two expressions that cannot both be cubes</title><link href="https://keivan-mirzaei.com/notes/two-expressions-that-cannot-both-be-cubes/" rel="alternate" type="text/html" title="Two expressions that cannot both be cubes" /><published>2026-09-30T00:00:00-06:00</published><updated>2026-09-30T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/two-expressions-that-cannot-both-be-cubes</id><author><name>Keivan Mirzaei</name></author><category term="number theory" /><category term="perfect powers" /><summary type="html"><![CDATA[For a natural number n, prove that n + 2 and n² + n + 1 cannot both be perfect cubes.]]></summary></entry><entry><title type="html">Conservative Polynomials</title><link href="https://keivan-mirzaei.com/notes/conservative-polynomials/" rel="alternate" type="text/html" title="Conservative Polynomials" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/conservative-polynomials</id><author><name>Keivan Mirzaei</name></author><category term="math" /><category term="algebra" /><category term="polynomials" /><summary type="html"><![CDATA[What happens to a polynomial when we take its absolute value?]]></summary></entry><entry><title type="html">Hilbert Matrices</title><link href="https://keivan-mirzaei.com/notes/hilbert-matrices/" rel="alternate" type="text/html" title="Hilbert Matrices" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/hilbert-matrices</id><author><name>Keivan Mirzaei</name></author><category term="math" /><category term="linear algebra" /><category term="analysis" /><summary type="html"><![CDATA[A deceptively simple matrix: can you prove it is always nonsingular?]]></summary></entry><entry><title type="html">Sampling Brownian Motion</title><link href="https://keivan-mirzaei.com/notes/sampling-brownian-motion/" rel="alternate" type="text/html" title="Sampling Brownian Motion" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/sampling-brownian-motion</id><author><name>Keivan Mirzaei</name></author><category term="code" /><category term="probability" /><category term="Python" /><category term="simulation" /><summary type="html"><![CDATA[From independent Gaussian increments to a sample path, with a small NumPy implementation.]]></summary></entry><entry><title type="html">Simple but Fun</title><link href="https://keivan-mirzaei.com/notes/simple-but-fun/" rel="alternate" type="text/html" title="Simple but Fun" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/simple-but-fun</id><author><name>Keivan Mirzaei</name></author><category term="math" /><category term="number theory" /><category term="parity" /><summary type="html"><![CDATA[A permutation of an odd-sized set produces an even product. Can you see why?]]></summary></entry><entry><title type="html">Stirling’s Approximation but Weaker</title><link href="https://keivan-mirzaei.com/notes/stirlings-approximation-but-weaker/" rel="alternate" type="text/html" title="Stirling’s Approximation but Weaker" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/stirlings-approximation-but-weaker</id><author><name>Keivan Mirzaei</name></author><category term="math" /><category term="analysis" /><category term="sequences" /><summary type="html"><![CDATA[Compare factorial and exponential growth by proving a limit.]]></summary></entry><entry><title type="html">Trigonometry Without a Word</title><link href="https://keivan-mirzaei.com/notes/trigonometry-without-a-word/" rel="alternate" type="text/html" title="Trigonometry Without a Word" /><published>2024-04-01T00:00:00-06:00</published><updated>2024-04-01T00:00:00-06:00</updated><id>https://keivan-mirzaei.com/notes/trigonometry-without-a-word</id><author><name>Keivan Mirzaei</name></author><category term="math" /><category term="geometry" /><category term="trigonometry" /><summary type="html"><![CDATA[Two arctangent identities, seen through a geometric proof without words.]]></summary></entry></feed>