Mean Value Theorem
Connects function values to derivative. Fundamental in analysis.
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Similar Mathematical Theorem
Fundamental Theorem of Calculus
Connects differential and integral calculus. Enables calculation of areas and rates.
Rolle's Theorem
Special mean value theorem. Critical points existence.
Divergence Theorem
Gauss theorem. Connects flux and divergence.
Intermediate Value Theorem
Intuitive but powerful. Guarantees roots exist.
Central Limit Theorem
Why normal distribution ubiquitous. Statistics foundation.
Stokes' Theorem
Generalizes fundamental theorem of calculus. Differential forms.
Banach-Tarski Paradox
Uses axiom of choice. Demonstrates measure theory limits.
Implicit Function Theorem
Guarantees existence of implicit functions. Crucial in multivariable calculus.
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Discover connections across different types of entities
Schrödinger Equation
Fundamental equation of quantum mechanics. Predicts probability distributions.
CPT Theorem
Fundamental symmetry of nature. Antimatter and time reversal.
Heisenberg Uncertainty Principle
Fundamental limit of measurement. Not about instruments but nature itself.
Existentialist perspective on meaning-making
Existentialist perspective on meaning-making
Wien's Displacement Law
Why hot objects change color. λmax = b/T.
Snell's Law
Refraction law. n₁sin(θ₁) = n₂sin(θ₂). Explains lenses.
Dialectic
Method of reasoning through opposition and resolution. Hegelian dialectic: thesis generates antithesis, resolved in synthesis …
Gauss's Law
Part of Maxwell's equations. Relates charge to electric field.