XerxesZorgon

import Mathlib

theorem sqrt_two_core {m n : ℕ} (h : m.Coprime n) : m ^ 2 ≠ 2 * n ^ 2 := by
  intro hmn
  -- 2 ∣ m², and 2 is prime, so 2 ∣ m
  have hm : 2 ∣ m := Nat.Prime.dvd_of_dvd_pow Nat.prime_two ⟨n ^ 2, hmn⟩
  obtain ⟨k, hk⟩ := hm
  -- substitute m = 2k and cancel a factor of 2
  have hk2 : 2 * k ^ 2 = n ^ 2 := by
    have : 2 * (2 * k ^ 2) = 2 * n ^ 2 := by rw [← hmn, hk]; ring

XerxesZorgon

{
 "cells": [
  {
   "kind": 1,
   "value": "## Bessel Functions in Three Dimensions",
   "languageId": "markdown",
   "outputs": [],
   "metadata": {}
  },
  {

XerxesZorgon

### A Pluto.jl notebook ###
# v1.0.3

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    return quote

XerxesZorgon

function rotating_squares(n_squares)
%ROTATING_SQUARES  Animate a chain of N squares linked at corners.
%
%  Geometry
%  --------
%  Each child square has sides 1/3 of its parent.  One corner of the child
%  is pinned to the top-right corner of the parent and rotates about that
%  pivot.  The child's angular speed is 3× the parent's, matching the
%  1:3 perimeter ratio (rolling-contact analogy for squares).
%

XerxesZorgon

using ModelingToolkit, OrdinaryDiffEq
include(joinpath(@__DIR__, "parameters.jl"))

# Independent variable
@independent_variableusing ModelingToolkit, OrdinaryDiffEq
include(joinpath(@__DIR__, "parameters.jl"))

# Independent variable
@independent_variables t

XerxesZorgon

# circular_equations.jl
# Numerical verification for "Circular Functions" — Wild Peaches
# Requires: Pkg.add("Polynomials")

using Polynomials

# ── 1. Cubic  3z³ − 9z² + 6z − 1 = 0,  z = x² ──────────────────
p = Polynomial([-1.0, 6.0, -9.0, 3.0])      # coefficients constant-first
z_poly = sort(real.(roots(p)))

XerxesZorgon

XerxesZorgon

package com.example.buckarootime

import android.Manifest
import android.content.pm.PackageManager
import android.os.Bundle
import android.os.Looper
import androidx.activity.ComponentActivity
import androidx.activity.compose.setContent
import androidx.activity.result.contract.ActivityResultContracts
import androidx.compose.foundation.layout.*

XerxesZorgon

XerxesZorgon

#=
Solves a geometry problem using linear algebra and Heron's formula
See: Red Flag Day Geometry

using Revise
Load with: includet("redflag.jl")

=#

using LinearAlgebra