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How a Lemniscate Became an Elliptic Curve

Posted by Nikitas Sotiropoulos on August 27, 2026

Elliptic Curves The lemniscate of Bernoulli

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A Small Taste from My New Book: Season 2 Episode 4

Posted by Nikitas Sotiropoulos on March 14, 2026

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Advanced Mathematics
Airy functions
Algorithms
Alternating series
Analytic continuation
Analytic number theory
Applications in Analysis and Number Theory
Archimedes
Arithmetic Geometry
Asymptotic Analysis

asymptotic behavior
Asymptotic formulas for Euler’s constant and the harmonic series
asymptotics
Audio synthesis
Bessel Functions
Big‑O Techniques
Borel Summation
Bounding Zero Fluctuations in the Critical Strip
C++
C++ programming
Canonical Products
Cauchy Theorem
Chebyshev–Mangoldt Function
Circles
Combinatorics
Complex Analysis
Complex Analysis Techniques
Complex Analysis Unveiled
Complex Plane Applications
Computational mathematics
Contour Deformation
Contour integration
Convergence Criteria for Infinite Products
Coprime Integers
Critical Strip Geometry
Digamma function
Dynamic programming
Education
Ellipses
Elliptic Curves
Elliptic Integrals
Entire Functions
episode guide
Euclid Algorithms
Euler–Maclaurin formula
Euler's Totient Function
Euler’s Totient Function
Exponential Decay
Exponential Integral
Farey Sequences
FFT
From Finite Sums to Analytic Continuation
Functional Equation
Gamma function
Genus of an Entire Function
Geometry
Greatest Common Divisor (GCD)
Growth of Analytic Functions
Hankel contour
Infinite Products in Complex Analysis
inverse Laplace
Inverse Laplace Transform
Inversion of points with respect to a circle
Jensen’s Formula as a Microscope
Keyhole contour
Landau function
Laplace inversion
Laplace transform
Laplace–Borel Transform
Laplace’s method
Lattice Points
Local Zero Analysis
Local Zero Density and Logarithmic Control
Logarithmic Derivative
Math Education
Mathematical algorithms
Mathematical Conjectures
Mathematical Connections
mathematical insights
Mathematical Mysteries
Mathematics
Meissel–Mertens constant
Mertens Function
Möbius Function
Möbius Inversion
Möbius transformations
Number theory
Order of an Entire Function
Oscillatory Functions
Perron’s Formula and Vanishing Tails
poles and residues
Poles and Singularities
Power Series
Prime numbers
Probability and Number Theory
Ramanujan
Rational Slopes
Reciprocals of Primes
Recursion History Of Math
Residue Calculus
Residue theorem
Riemann Hypothesis
Riemann zeta
Riemann Zeta Function
Series Expansion and Asymptotics
Signal processing
Sonification
special functions
Spectral analysis
Steepest descent
Stirling's formula
Structure of Arithmetic Functions
The Airy Integral
The Essential Transform Toolkit
The Geometry Behind the Airy Function
The lemniscate of Bernoulli
The observable universe
The point of controlled zero distance
Theory Meets Practice
Transform Calculus
Transform methods
Transform Toolkit
Transforms
Visible Points
Watson’s Lemma
Well-spaced ordinate estimate
Where Complex Analysis Reveals Its Power
Zeros of Entire Functions
Zeros of the Riemann Zeta Function
Zeta Function
Zeta Logarithmic Derivative Estimates
Zeta Zeros

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Most Popular

From Archimedes to Infinity

Circles, Ellipses, and Elliptic Integrals

How a Lemniscate Became an Elliptic Curve

The lemniscate of Bernoulli

Why 6/π² Appears When Counting Visible Lattice Points (and Why π² Is Actually From Earth)

A lattice point is a point in the Cartesian plane whose - and -coordinates are both integers.

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