Nikolay Eremeev — SandboxInteractive articles on matroids, proofs and Spark internals.https://nikolay-eremeev.com/en-usWhat is a matroid? Definition, examples, and why greedy workshttps://nikolay-eremeev.com/sandbox/matroid/https://nikolay-eremeev.com/sandbox/matroid/What a matroid is, in plain terms: the exchange axiom, graphic, linear and uniform examples you can click, and why greedy is optimal exactly on matroids.Sat, 13 Jun 2026 00:00:00 GMTmathcombinatoricsmatroidgreedyvisualizationCSR: How Graphs Are Stored in Flat Arrayshttps://nikolay-eremeev.com/sandbox/csr-format/https://nikolay-eremeev.com/sandbox/csr-format/Interactive visualization of Compressed Sparse Row: three flat arrays replace nested hash maps for sparse graphs, for 10-30x speedups from cache locality.Sun, 12 Apr 2026 00:00:00 GMTdata-structuresgraphsperformancevisualizationPythagorean Theorem: Visual Proofhttps://nikolay-eremeev.com/sandbox/pythagorean-theorem/https://nikolay-eremeev.com/sandbox/pythagorean-theorem/An interactive visual proof of the Pythagorean theorem using area rearrangement of four identical right triangles inside a square.Thu, 15 Jan 2026 00:00:00 GMTmathgeometryproofvisualizationProof that √2 is Irrational: Interactive Walkthroughhttps://nikolay-eremeev.com/sandbox/sqrt2-irrational/https://nikolay-eremeev.com/sandbox/sqrt2-irrational/Interactive step-by-step proof by contradiction that the square root of 2 cannot be expressed as a ratio of two integers.Wed, 14 Jan 2026 00:00:00 GMTmathnumber-theoryproofvisualizationCantor's Diagonal Argument: ℝ is Uncountablehttps://nikolay-eremeev.com/sandbox/cantor-diagonal/https://nikolay-eremeev.com/sandbox/cantor-diagonal/Interactive visualization of Cantor's diagonal argument proving that the set of real numbers is uncountable — there is no bijection between ℕ and ℝ.Tue, 13 Jan 2026 00:00:00 GMTmathset-theoryproofvisualizationApache Spark RDD Transformations Pipelinehttps://nikolay-eremeev.com/sandbox/spark-rdd/https://nikolay-eremeev.com/sandbox/spark-rdd/Interactive visualization of how Apache Spark RDD transformations form a lazy evaluation pipeline — map, filter, and reduce operations on distributed data.Mon, 12 Jan 2026 00:00:00 GMTdistributed-systemssparkrddvisualizationSpark Fault Tolerance via RDD Lineagehttps://nikolay-eremeev.com/sandbox/spark-fault-tolerance/https://nikolay-eremeev.com/sandbox/spark-fault-tolerance/Interactive visualization of how Apache Spark recovers from executor failures using RDD lineage — recomputing lost partitions from their transformation history.Sun, 11 Jan 2026 00:00:00 GMTdistributed-systemssparkfault-tolerancevisualizationSpark DAG Scheduler: From Logical Plan to Physical Executionhttps://nikolay-eremeev.com/sandbox/spark-dag-scheduler/https://nikolay-eremeev.com/sandbox/spark-dag-scheduler/Interactive visualization of how Spark's DAG scheduler turns a logical plan into stages and tasks, cutting stage boundaries at each shuffle point.Sat, 10 Jan 2026 00:00:00 GMTdistributed-systemssparkschedulervisualizationEMR YARN Dynamic Executor Allocationhttps://nikolay-eremeev.com/sandbox/emr-yarn-allocation/https://nikolay-eremeev.com/sandbox/emr-yarn-allocation/Interactive visualization of how Amazon EMR with YARN scales Spark executors up and down with workload demand, balancing utilization against cost.Fri, 09 Jan 2026 00:00:00 GMTdistributed-systemssparkyarnemrvisualization