tpogden

x	y	c
15.55	28.65	2
14.9	27.55	2
14.45	28.35	2
14.15	28.8	2
13.75	28.05	2
13.35	28.45	2
13	29.15	2
13.45	27.5	2
13.6	26.5	2

tpogden

x	y	c
0.85	17.45	2
0.75	15.6	2
3.3	15.45	2
5.25	14.2	2
4.9	15.65	2
5.35	15.85	2
5.1	17.9	2
4.6	18.25	2
4.05	18.75	2

tpogden

0.85	17.45	2
0.75	15.6	2
3.3	15.45	2
5.25	14.2	2
4.9	15.65	2
5.35	15.85	2
5.1	17.9	2
4.6	18.25	2
4.05	18.75	2
3.4	19.7	2

tpogden

# ! python
# coding: utf-8

import os
import argparse
import glob

import nbformat
from nbconvert.preprocessors import ExecutePreprocessor
from nbconvert.preprocessors.execute import CellExecutionError

tpogden

height: 944
border: no

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The ⊗ icon I use on tommyogden.com, made in D3.

tpogden

Monte Carlo integration of the function $f(x) = x^2$ on the interval $\left[ 0, 1 \right]$ on $\mathbb{R}$. The correct result is $1/3$. How close is the numerically computed result?

We sample $N = 1000$ points on the plane $(x,y) \in ([0,1], [0,1])$ and define an acceptance function

$$ A(x,y) = \begin{cases} 1 & \text{if} ~ y \leq f(x) \

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Plots the first ten Hermite polynomials (physicists' definition), defined using the recursion relation.

$$ H_{n+1}(x) = 2x H_n(x) - 2 (n-1) H_{n-2}(x) $$

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Fits a straight line to data using the Least Squares method.

"Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.

Least squares function by Ben van Dyke.

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A set of 100 points are given a new uniform random distribution every 5 seconds.