{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# OpenLearn Geometry\n", "\n", "\n", "This notebook recreates some of the content featured in the OpenLearn course [*Geometry*](http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics-education/geometry/content-section-0?active-tab=content-tab).\n", "\n", "The notebook includes several hidden code cells that generate the a range of geometric figures.\n", "\n", "To render the images, go to the *Cell* menu and select *Run All*.\n", "\n", "To view/hide the code used to generate the figures, click on the *Hide/Reveal Code Cell Inputs* button in the notebook toolbar.\n", "\n", "To make changes to the diagrams, click in the appropriate code input cell, make your change, and then run the cell using the *Run Cell* (\"Play\") button in the toolbar or via the keyboard shortcut SHIFT-ENTER.\n", "\n", "Entering Ctrl-Z (or CMD-Z) in the code cell will undo your edits..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Angles\n", "\n", "The [*Try some yourself*](http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics-education/geometry/content-section-1.1.1) activity includes the following shape." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "hide_input": true }, "outputs": [], "source": [ "%load_ext tikz_magic" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide_input": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz\n", "\\usetikzlibrary{positioning}\n", "\n", "\\coordinate (A) at (0,0) ;\n", "\\coordinate (B) at (5,0.3) ;\n", "\\coordinate (C) at (4.5,-2) ;\n", "\\coordinate (D) at (2,-3) ;\n", "\n", "\n", "\\draw (A) node[left]{A} -- (B)node[right]{B};\n", "\\draw (B) -- (C)node[right]{C};\n", "\\draw (C) -- (A) ;\n", "\\draw (A) -- (D) node[below]{D};\n", "\\draw (D) -- (C);\n", "\n", "\n", "\\begin{scope}\n", " \\clip (B) -- (A) -- (C);\n", " \\draw (A) circle[radius=1.1];\n", "\\end{scope}\n", "\\node at (A)[below right=-0.05 and 0.5 ] {$\\alpha$};\n", "\n", "\\begin{scope}\n", " \\clip (C) -- (A) -- (D);\n", " \\draw (A) circle[radius=1.1];\n", "\\end{scope}\n", "\\node at (A)[below right=0.3 and 0.3 ] {$\\gamma$};\n", "\n", "\\begin{scope}\n", " \\clip (B) -- (C) -- (A);\n", " \\draw (C) circle[radius=1];\n", "\\end{scope}\n", "\\node at (C)[above left=0.25 and 0.2 ] {$\\beta$};\n", "\n", "\n", "\\begin{scope}\n", " \\clip (A) -- (C) -- (D);\n", " \\draw (C) circle[radius=1];\n", "\\end{scope}\n", "\\node at (C)[left=0.4 ] {$\\delta$};" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometric shapes – circles\n", "\n", "[Original link](http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics-education/geometry/content-section-2.3)\n", "\n", "All circles are the same shape – they can only have different sizes.\n", "\n", "In a circle, all the points are the same distance from a point called the centre. The centre is often labelled with the letter O." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide_input": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz\n", "%https://tex.stackexchange.com/a/223219\n", "\n", "\\def\\radius{2}% radius of the circle\n", "\\def\\tilt{30}% angle for the arc\n", "\n", "%origin\n", "\\coordinate (O) at (0,0) ;\n", "\n", "% Circle\n", "\\draw (O) circle[radius=\\radius] node[font=\\tiny, right]{{\\em{O}} (Centre)};\n", "\n", "%Centre point\n", "\\draw[black,fill=black] (0,0) circle [radius=0.03];\n", "\n", "%Diameter\n", "%latex-latex defines the 'latex' arrow head at each end of the line\n", "\\draw[latex-latex ] (\\tilt:\\radius) -- (180+\\tilt:\\radius)\n", " node[font=\\tiny,above, midway,rotate=\\tilt]{Diameter};\n", "\n", "%Radius\n", "\\draw[latex-latex ] (O) -- (\\tilt+270:\\radius)\n", " node[font=\\tiny,above, midway, above right]{Radius};\n", "\n", "%Circumference \n", "\\draw (\\tilt+30:\\radius) -- +(0.5,1) -- +(0.75,1) node [right]{\\tiny{Circumference}} ;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The outside edge of a circle is called the __circumference__. A straight line from the centre to a point on the circumference is called a __radius__ of the circle (the plural of radius is radii).\n", "\n", "A line with both ends on the circumference and passing through the centre is called a __diameter__. Any diameter cuts the circle into two halves called __semicircles__." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hide_input": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz\n", "% Define radius\n", "\\def\\radius{1.5}\n", "\n", "%origin\n", "\\coordinate (O) at (0,0) ;\n", "\\path (O) +(\\radius,0) coordinate (arcOrigin);\n", " \n", "%Draw dashed semi-circle\n", "\\draw [dashed] (arcOrigin) arc(0:-180:\\radius);\n", "\n", "%Draw grey semicircle - the -- cycle component closes the shape\n", "\\draw [fill={black!30}] (arcOrigin) arc(0:180:\\radius) \n", " %Close the figure and add a diameter label\n", " -- cycle node [font=\\tiny,below,midway]{Diameter};\n", "\n", "%Centre point\n", "\\draw[black,fill=black] (O) circle [radius=0.03];\n", "\n", "%Circumference label - build a relative line to connent circumference and label\n", "\\draw (30:\\radius) -- ++(0.5,1) -- +(0.25,0) node [font=\\tiny,right,\n", " align=left]{Half the \\\\ circumference} ;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the circle below, the lines labelled OA, OB, OC, OD and OE are all radii, and AD and BE are diameters. The points A, B, C, D and E all lie on the circumference." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide_input": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz\n", "\n", "\\def\\radius{2}% radius of the circle\n", "\n", "%origin\n", "\\coordinate (O) at (0,0) ;\n", "\n", "% Circle\n", "\\draw (O) circle[radius=\\radius] node[font=\\tiny, left]{\\em{O}};\n", "\n", "%Centre point\n", "\\draw[black,fill=black] (0,0) circle [radius=0.03];\n", "\n", "\\draw (O) -- (125:\\radius) node[font=\\tiny,above]{A};\n", "\\draw (O) -- (60:\\radius) node[font=\\tiny,above right]{B};\n", "\\draw (O) -- (0:\\radius) node[font=\\tiny,right]{C};\n", "\\draw (O) -- (-50:\\radius) node[font=\\tiny,right]{D};\n", "\\draw (O) -- (-140:\\radius) node[font=\\tiny,left]{E};" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the terms ‘radius’, ‘diameter’ and ‘circumference’ each denote a certain line, these words are also employed to mean the lengths of those lines. So it is common to say, for example, ‘Mark a point on the circumference’ and ‘The circumference of this circle is 7.3 cm’. It is obvious from the context whether the line itself or the length is being referred to." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extra Examples\n", "\n", "Handy fragments from Stack Overflow.." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz\n", "%https://tex.stackexchange.com/a/197711\n", "\\path (120:3) coordinate (A) (0:3) coordinate (B) (0:0) coordinate (C);\n", "\\draw (A) \n", " -- (B) node [at start, above left] {$A$} node [midway, above] {$c$}\n", " -- (C) node [at start, right] {$B$} node [midway, below] {$a$}\n", " -- (A) node [at start, below] {$C$} node [midway, below] {$b$}\n", " -- cycle;\n", "\\draw [dashed] (A) |- (C) node [midway, below left] {$P$}; \n", "\n", "%The -- (60:.6) element adds the tick to the angle\n", "\\draw (0:.5) arc (0:120:.5) (60:.4) -- (60:.6);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%tikz --no-wrap\n", "%via https://tex.stackexchange.com/a/397793/151162\n", "\\usetikzlibrary{angles,quotes}\n", "\n", "\\begin{tikzpicture}[x=4cm, y=4cm, axes/.style={thin, gray, ->},\n", " dot/.style={.. dot={#1:0:;}}, \n", " .. dot/.style args={#1:#2:#3;}{insert path={ \n", " coordinate (#1) \n", " node [circle, fill, inner sep=0, minimum size=2pt,label=#2:#1]{}\n", " }}]\n", "\\clip (-0.25, -0.25) rectangle (1.5,1.5);\n", "\\draw[axes] (-1.2,0) -- (1.2,0) node[right] {$x$};\n", "\\draw[axes] (0,-1.2) -- (0,1.2) node[above] {$y$};\n", "\\def\\a{40}\n", "\\path\n", " (0,0) [dot=O:225] \n", " (0:1) [dot=A:315]\n", " (\\a:1) [dot=B:90] \n", " (0:cos \\a) [dot=C:270]\n", " (\\a:sec \\a) [dot=D]\n", " (1, cosec \\a-cot \\a) [dot=E];\n", "\\draw (O) circle[radius=1];\n", "\\draw (O) -- (B) -- (C);\n", "\\draw (B) -- (D) -- (A);\n", "\\draw [dashed] (B) -- (A);\n", "\\draw [dashed] (B) -- (E);\n", "\\pic [\"$\\theta$\", draw, ->, angle radius=1cm] {angle=C--O--B};\n", "\\path (O) -- (B) node [midway, above] {$1$};\n", "\\path (O) -- (C) node [midway, below] {$\\cos\\theta$};\n", "\\end{tikzpicture}\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": true, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 2 }