{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### 半径1の円に内接する正N角形の面積と円周率\n", "\n", "> Tags\n", "\n", "- limits\n", "- pi\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "vscode": { "languageId": "wolfram" } }, "outputs": [ { "data": { "text/html": [ "
13.2.0 for Linux x86 (64-bit) (December 12, 2022)
" ], "text/plain": [ "13.2.0 for Linux x86 (64-bit) (December 12, 2022)" ] }, "execution_count": 1, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "$Version" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "vscode": { "languageId": "wolfram" } }, "outputs": [], "source": [ "BoxForm`$UseTemplateSlotSequenceForRow = False;" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "> 半径1の円に内接する正$n$角形の面積\n", "\n", "半径1の円に内接する正$n$角形の面積を$S_n$とすると\n", "\n", "$$\n", "S_n = \\frac{n}{2} \\times \\sin \\frac{2\\pi}{n}\n", "$$\n", "\n", "半径1の円の面積は$\\pi$なので以下のことが予想される\n", "\n", "$$\n", "\\lim_{n\\to\\infty} S_n = \\pi\n", "$$\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "vscode": { "languageId": "wolfram" } }, "outputs": [ { "data": { "text/html": [ "
\"Output\"
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