SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
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SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
1.26K subscribers
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#notation
source
John D. Cook | Applied Mathematics Consulting
Annuity and factorial notation
Two uses of bracket notation: actuarial symbols related to annuities and an obsolete notation for factorial
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Combinatorics
source
John D. Cook | Applied Mathematics Consulting
Analogs of binomial coefficients
Numbers like binomial coefficients satisfy identities like Pascal's triangle.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Theory
of
#Interest
source
John D. Cook | Applied Mathematics Consulting
Taylor Series and the Argentine Peso
Present value approximation that implicitly assumes moderate interest rates gives absurd results when applied at high interest rates.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Python
#Cryptography
#Elliptic_curves
#SymPy
source
John D. Cook | Applied Mathematics Consulting
Monero’s elliptic curve
Exploring the elliptic curve used in Monero for digital signatures. Making explicit some things that are often left implicit.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Cryptography
#Elliptic_curves
source
John D. Cook | Applied Mathematics Consulting
Equivalence between commonly used elliptic curves
The elliptic curves Ed25519 and Curve25519 are both used in cryptography, and are equivalent in one sense and not in another.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Number_theory
source
John D. Cook | Applied Mathematics Consulting
Moessner’s Magic
Moessner's Magic is a generalization of an ancient theorem that wasn't discovered until 1951.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Differential_equations
source
John D. Cook | Applied Mathematics Consulting
The sound of drums that tile the plane
Bounds on the frequencies of a vibrating membrane, provided its shape can tile the plane.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Geometry
#Number_theory
source
John D. Cook | Applied Mathematics Consulting
Primitive Pythagorean triangles with the same area
You can find three primitive Pythagorean triangles with the same area, but what about four?
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Geometry
source
John D. Cook | Applied Mathematics Consulting
Finding tangent circles | Descartes theorem
Given three mutually tangent circles, there is an elegant theorem for finding two more circles tangent to all three.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Cryptocurrency
#Cryptography
#Elliptic_curves
source
John D. Cook | Applied Mathematics Consulting
Whimsical elliptic curves in Zcash zero knowledge proofs
Several elliptic curves which Zcash uses in zero knowledge proofs are named after characters from Lewis Carroll: Jubjub, Bandersnatch, Tweddledee, Tweedledum
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Cryptocurrency
#Elliptic_curves
source
John D. Cook | Applied Mathematics Consulting
Pallas and Vesta elliptic curves used in Zcash
Two elliptic curves used in Zcash for zero-knowledge proofs, one named after a Greek goddess of war and one after a Roman goddess of home and hearth
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Elliptic_curves
source
John D. Cook | Applied Mathematics Consulting
Cycles of Elliptic Curves
Cycles of ellptic curves have the property that the number of points on one curve equals the field size of the next curve.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Mathematica
#Number_theory
#SymPy
source
John D. Cook | Applied Mathematics Consulting
Time to factor big integers Python and Mathematica
Testing the time to factor big integers in Python with SymPy compared to Matheamtica
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
source
John D. Cook | Applied Mathematics Consulting
Making the two-dimensional one-dimensional
We often want to reduce something that's inherently two-dimensional into something one-dimensional. We want to turn graph into a list. And we'd like to do this with some kind of faithfulness. We'd like things that are close together in 2D space to be close…
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Elliptic
#curves
source
John D. Cook | Applied Mathematics Consulting
Counting points on an elliptic curve
Counting the number of points on an elliptic curve using a crude algorithm, a better algorithm, and the best algorithm.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Memory
#Number_theory
source
John D. Cook | Applied Mathematics Consulting
Prime numbers that are easy to remember
Memorable prime numbers with various numbers of digits. For example, if you need a five-digit prime, you could say 18181.
SATOSHI ° NOSTR ° AI LLM ML ° LINUX ° MESH ° BUSINESS | HODLER TUTORIAL
#Math
#Cryptography
#Elliptic_curves
source
John D. Cook | Applied Mathematics Consulting
Misleading plots of elliptic curves
Plotting the points on an elliptic curve over a finite field can be very misleading.