diff --git a/.husky/pre-commit b/.husky/pre-commit index d0a8bed..cf03b66 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -2,5 +2,5 @@ . "$(dirname "$0")/_/husky.sh" npx pretty-quick --staged -node .husky/scripts/cleanMaths.js +.husky/scripts/pdfToPng.sh git add . diff --git a/.husky/scripts/cleanMaths.js b/.husky/scripts/cleanMaths.js deleted file mode 100644 index 99170a5..0000000 --- a/.husky/scripts/cleanMaths.js +++ /dev/null @@ -1,73 +0,0 @@ -const fs = require('fs'); -const path = require('path'); -const { pdfToPng } = require('pdf-to-png-converter'); -const Jimp = require('jimp'); - -const mathsDir = path.resolve(__dirname, '..', '..', 'maths'); - -const cropBuffer = buffer => - new Promise((resolve, reject) => { - Jimp.read(buffer) - .then(cropped => { - cropped.autocrop(); - - new Jimp( - cropped.getWidth() + 100, - cropped.getHeight() + 100, - '#ffffff', - async (err, image) => { - if (err) reject(err); - - image.blit(cropped, 50, 50); - - resolve(await image.getBufferAsync(Jimp.MIME_PNG)); - } - ); - }) - .catch(err => reject(err)); - }); - -const crawlDirectory = async dir => { - const dirents = fs.readdirSync(dir, { withFileTypes: true }); - - const files = await Promise.all( - dirents.map(dirent => { - const res = path.resolve(dir, dirent.name); - return dirent.isDirectory() ? crawlDirectory(res) : res; - }) - ); - - return files.flat(); -}; - -(async () => { - const files = await crawlDirectory(mathsDir); - - files.forEach(file => { - const [filePath, fileDirectory, fileNameWithExt] = file.match(/(.*)\/((?:.(?!\/))+)$/); - const [fileName, fileExtension] = fileNameWithExt.split('.'); - - if (file.endsWith('.pdf')) { - pdfToPng(filePath).then(async output => { - const pageCount = output.length; - - if (pageCount > 1) - output.forEach(async (page, i) => - fs.writeFileSync( - path.join(fileDirectory, `${fileName}-${i + 1}.png`), - await cropBuffer(page.content) - ) - ); - else - fs.writeFileSync( - path.join(fileDirectory, `${fileName}.png`), - await cropBuffer(output[0].content) - ); - }); - } - - if (fileExtension !== 'tex' && fileExtension !== 'png' && fileExtension !== 'cls') { - fs.rmSync(filePath); - } - }); -})(); diff --git a/.husky/scripts/pdfToPng.sh b/.husky/scripts/pdfToPng.sh new file mode 100755 index 0000000..3a2a04d --- /dev/null +++ b/.husky/scripts/pdfToPng.sh @@ -0,0 +1,22 @@ +#!/bin/bash +find . -print0 | while IFS= read -r -d '' file +do + if [ -f "$file" ]; then + if [[ $file == *pdf ]]; then + mkdir temp + gm convert "$file" +adjoin temp/temp%02d.png + + for temp in ./temp/*.png + do + gm convert "$temp" -fuzz 80% -trim +repage -bordercolor white -border 50x25 "$temp" + done + + readarray -d . -t arr <<< $file + + gm convert -append ./temp/*.png "${arr[1]:1}.png" + + rm -rf temp + rm "$file" "${arr[1]:1}.synctex.gz" + fi +fi +done diff --git a/maths/halley's method.png b/maths/halley's method.png new file mode 100644 index 0000000..bec432b Binary files /dev/null and b/maths/halley's method.png differ diff --git a/maths/halley's method.tex b/maths/halley's method.tex new file mode 100644 index 0000000..4aa714a --- /dev/null +++ b/maths/halley's method.tex @@ -0,0 +1,53 @@ +\documentclass{style} +\usepackage{amsmath} +\usepackage{breqn} +\usepackage{mathtools} + +\begin{document} +\begin{center} + Suppose we have an $n$th degree polynomial, such that $f(x) = c_{n}x^{n} + c_{n-1}x^{n-1} + c_{n-2}x^{n-2} + ... + c_{0} = \sum_{i=0}^{n}c_{n-i}x^{n-i}$ + + \hfill + + By the power rule of differentiation, we can conclude that the first derivative of $f(x)$ is as follows + + \begin{dmath*} + f'(x) = nc_{n}x^{n-1} + (n-1)c_{n-1}x^{n-2} + (n-2)c_{n-2}x^{n-3} + ... + c_{1} = \sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1} + \end{dmath*} + + And the second derivative is + + \begin{dmath*} + f''(x) = n(n-1)c_{n}x^{n-2} + (n-1)(n-2)c_{n-1}x^{n-3} + (n-2)(n-3)c_{n-2}x^{n-4} + ...+ c_{2} = \sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2} + \end{dmath*} + + After starting with an initial guess, the next iteration of Halley's method is given by $x_k - \frac{2f(x_k)f'(x_k)}{2[f'(x_k)]^2 - f(x_k)f''(x_k)}$. + + This means that we must first find $f(x)f'(x)$, $[f'(x)]^2$, and $f(x)f''(x)$. These all consist of the multiplication of two series - there is a nice general form to this problem stated below + + \begin{dmath*} + (\sum_{i=0}^{n}x_{i})(\sum_{j=0}^{m}y_{j}) = \sum_{i=0}^{n}\sum_{j=0}^{m}x_iy_j + \end{dmath*} + + \newpage + From this, we can conclude that: + + \begin{dmath*} + f(x)f'(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1} + \end{dmath*} + + \begin{dmath*} + [f'(x)]^2 = (\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j} + \end{dmath*} + + \begin{dmath*} + f(x)f''(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2}) = \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j} + \end{dmath*} + + And all that is left to do is to plug it into the formula for Halley's method, leaving us with the following: + + \begin{align*} + x_{k+1} = x_{k} - \dfrac{2\sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1}}{\splitdfrac{2\sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}{- \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}} + \end{align*} +\end{center} +\end{document} diff --git a/maths/nth root.png b/maths/nth root.png index 20e0269..72b7276 100644 Binary files a/maths/nth root.png and b/maths/nth root.png differ diff --git a/maths/style.cls b/maths/style.cls index 0ae58c8..7d8f991 100644 --- a/maths/style.cls +++ b/maths/style.cls @@ -1,6 +1,9 @@ \LoadClass[17pt]{extarticle} \pagenumbering{gobble} +\usepackage{geometry} +\geometry{a4paper, portrait, margin=1in} + \newcommand{\euler}{\begin{gather*} \text{By Euler's formula:} \\ e^{i\theta} = cos(\theta) + i\sin(\theta) \\ diff --git a/maths/trigometric functions/cos.png b/maths/trigometric functions/cos.png index 3aabec7..08cb715 100644 Binary files a/maths/trigometric functions/cos.png and b/maths/trigometric functions/cos.png differ diff --git a/maths/trigometric functions/cot-1.png b/maths/trigometric functions/cot-1.png deleted file mode 100644 index 9a62e0d..0000000 Binary files a/maths/trigometric functions/cot-1.png and /dev/null differ diff --git a/maths/trigometric functions/cot-2.png b/maths/trigometric functions/cot-2.png deleted file mode 100644 index 2e2d9e0..0000000 Binary files a/maths/trigometric functions/cot-2.png and /dev/null differ diff --git a/maths/trigometric functions/cot.png b/maths/trigometric functions/cot.png new file mode 100644 index 0000000..24e5ef0 Binary files /dev/null and b/maths/trigometric functions/cot.png differ diff --git a/maths/trigometric functions/csc-1.png b/maths/trigometric functions/csc-1.png deleted file mode 100644 index bfd7616..0000000 Binary files a/maths/trigometric functions/csc-1.png and /dev/null differ diff --git a/maths/trigometric functions/csc-2.png b/maths/trigometric functions/csc-2.png deleted file mode 100644 index f06b898..0000000 Binary files a/maths/trigometric functions/csc-2.png and /dev/null differ diff --git a/maths/trigometric functions/csc.png b/maths/trigometric functions/csc.png new file mode 100644 index 0000000..42d3774 Binary files /dev/null and b/maths/trigometric functions/csc.png differ diff --git a/maths/trigometric functions/sec-1.png b/maths/trigometric functions/sec-1.png deleted file mode 100644 index b5a71f7..0000000 Binary files a/maths/trigometric functions/sec-1.png and /dev/null differ diff --git a/maths/trigometric functions/sec-2.png b/maths/trigometric functions/sec-2.png deleted file mode 100644 index 0fed58a..0000000 Binary files a/maths/trigometric functions/sec-2.png and /dev/null differ diff --git a/maths/trigometric functions/sec.png b/maths/trigometric functions/sec.png new file mode 100644 index 0000000..75793b7 Binary files /dev/null and b/maths/trigometric functions/sec.png differ diff --git a/maths/trigometric functions/sin.png b/maths/trigometric functions/sin.png index 50f9ede..a9f8b47 100644 Binary files a/maths/trigometric functions/sin.png and b/maths/trigometric functions/sin.png differ diff --git a/maths/trigometric functions/tan-1.png b/maths/trigometric functions/tan-1.png deleted file mode 100644 index de63b2b..0000000 Binary files a/maths/trigometric functions/tan-1.png and /dev/null differ diff --git a/maths/trigometric functions/tan-2.png b/maths/trigometric functions/tan-2.png deleted file mode 100644 index ba54fb9..0000000 Binary files a/maths/trigometric functions/tan-2.png and /dev/null differ diff --git a/maths/trigometric functions/tan.png b/maths/trigometric functions/tan.png new file mode 100644 index 0000000..1165f85 Binary files /dev/null and b/maths/trigometric functions/tan.png differ diff --git a/package.json b/package.json index e974973..d1153d6 100644 --- a/package.json +++ b/package.json @@ -1,16 +1,13 @@ { "name": "the-honk", "scripts": { - 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