# ProofWiki:Potw

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## Current Featured Proof

### HOW TO USE THIS PAGE

- $(1): \quad$ Select the proof $\text P$ you want to put up as POTW.
- $(2): \quad$ Edit $\text P$ to put this at the top:

`<!--{{Previous POTW|<today>}}-->`

- replacing
`<today>`with today's date.

- $(3): \quad$ Edit the previous POTW to change:
`<!--{{Previous POTW|<somedate>}}-->`

- to:
`{{Previous POTW|<somedate>|<today>}}`

- $(4): \quad$ Edit
**this**page to:- $\text {(a)}$ add the old POTW to the top of the list
- $\text {(b)}$ put the new POTW into the two places where the last one was.

- $(5): \quad$ Purge the main page (or edit it and save it without changes) to refresh the page.

### Previous featured proofs

- Real Plus Epsilon
- Generalized Integration by Parts
- Harmonic Number is not Integer
- Length of Perimeter of Cardioid
- Number of Primes is Infinite
- Complex Numbers cannot be Ordered Compatibly with Ring Structure
- Length of Arc of Astroid
- Area of Triangle in Terms of Circumradius
- Fundamental Theorem of Calculus/Second Part/Proof 2
- Brahmagupta-Fibonacci Identity
- Primitive of Reciprocal of x squared plus a squared/Arctangent Form
- Intersection of Relation with Inverse is Symmetric Relation
- Between two Real Numbers exists Rational Number
- De Méré's Paradox
- Cauchy Condensation Test
- Congruence of Sum of Digits to Base Less 1
- Rule of Material Implication/Formulation 1
- Identity of Points
- Differentiable Function is Continuous
- Harmonic Series is Divergent/Proof 1
- Square Root of 2 is Irrational/Classic Proof
- Difference Between Adjacent Square Roots Converges
- Image of Intersection under One-to-Many Relation
- Fundamental Theorem on Equivalence Relations
- Linear Transformation as Matrix Product
- König's Tree Lemma
- Mean Value Theorem
- Brahmagupta Theorem
- Orbit-Stabilizer Theorem
- Variance as Expectation of Square minus Square of Expectation
- Integrating Factor for First Order ODE
- Cassini's Identity
- Bayes' Theorem
- Solution to Linear First Order Ordinary Differential Equation
- Basis Representation Theorem
- Odd Number Theorem
- Euler's Number is Irrational
- Kleene's Normal Form Theorem
- Picard's Existence Theorem
- Fundamental Theorem of Arithmetic
- Peak Point Lemma
- Closed Form for Triangular Numbers
- Existence of Euler-Mascheroni Constant
- Cauchy Mean Value Theorem
- Sum of Angles of Triangle equals Two Right Angles
- Monotone Convergence Theorem (Real Analysis)
- Bhaskara's Lemma
- Conjugacy Class Equation
- Fermat's Two Squares Theorem
- L'Hôpital's Rule
- Banach-Tarski Paradox
- Rolle's Theorem
- Heron's Formula
- Area of Circle
- Zero and One are the only Consecutive Perfect Squares/Proof 1
- Chinese Remainder Theorem/General Result
- Sigma Function is Multiplicative
- Euclid's Lemma for Prime Divisors
- Lebesgue's Number Lemma
- Cardano's Formula
- Area of Square
- Integration by Parts
- Euclid's Lemma
- Combination Theorem for Sequences
- Russell's Paradox
- Derivative of Composite Function
- First Sylow Theorem
- Euler Phi Function of Integer
- Fundamental Principle of Counting
- Partition Equation
- Archimedean Principle
- Pascal's Rule
- Division Theorem
- Lagrange's Theorem (Group Theory)
- Solution to Quadratic Equation
- Handshake Lemma
- Cantor-Bernstein-Schröder Theorem
- Euler's Formula
- Fermat's Little Theorem
- Cantor's Theorem
- Euclid's Theorem
- Binomial Theorem
- Existence of Rational Powers of Irrational Numbers
- Law of Cosines
- Pythagoras's Theorem

## Also see

`{{Previous POTW}}`

`{{POTW Candidate}}`