\documentclass[12pt,titlepage]{article} \usepackage{amsmath} \usepackage{mathrsfs} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage{mathtools} \usepackage{graphicx} \usepackage{color} \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage{xparse} \usepackage{tikz} \usepackage{hyperref} %----Macros---------- % % Unresolved issues: % % \righttoleftarrow % \lefttorightarrow % % \color{} with HTML colorspec % \bgcolor % \array with options (without options, it's equivalent to the matrix environment) % Of the standard HTML named colors, white, black, red, green, blue and yellow % are predefined in the color package. Here are the rest. \definecolor{aqua}{rgb}{0, 1.0, 1.0} \definecolor{fuschia}{rgb}{1.0, 0, 1.0} \definecolor{gray}{rgb}{0.502, 0.502, 0.502} \definecolor{lime}{rgb}{0, 1.0, 0} \definecolor{maroon}{rgb}{0.502, 0, 0} \definecolor{navy}{rgb}{0, 0, 0.502} \definecolor{olive}{rgb}{0.502, 0.502, 0} \definecolor{purple}{rgb}{0.502, 0, 0.502} \definecolor{silver}{rgb}{0.753, 0.753, 0.753} \definecolor{teal}{rgb}{0, 0.502, 0.502} % Because of conflicts, \space and \mathop are converted to % \itexspace and \operatorname during preprocessing. % itex: \space{ht}{dp}{wd} % % Height and baseline depth measurements are in units of tenths of an ex while % the width is measured in tenths of an em. \makeatletter \newdimen\itex@wd% \newdimen\itex@dp% \newdimen\itex@thd% \def\itexspace#1#2#3{\itex@wd=#3em% \itex@wd=0.1\itex@wd% \itex@dp=#2ex% \itex@dp=0.1\itex@dp% \itex@thd=#1ex% \itex@thd=0.1\itex@thd% \advance\itex@thd\the\itex@dp% \makebox[\the\itex@wd]{\rule[-\the\itex@dp]{0cm}{\the\itex@thd}}} \makeatother % \tensor and \multiscript \makeatletter \newif\if@sup \newtoks\@sups \def\append@sup#1{\edef\act{\noexpand\@sups={\the\@sups #1}}\act}% \def\reset@sup{\@supfalse\@sups={}}% \def\mk@scripts#1#2{\if #2/ \if@sup ^{\the\@sups}\fi \else% \ifx #1_ \if@sup ^{\the\@sups}\reset@sup \fi {}_{#2}% \else \append@sup#2 \@suptrue \fi% \expandafter\mk@scripts\fi} \def\tensor#1#2{\reset@sup#1\mk@scripts#2_/} \def\multiscripts#1#2#3{\reset@sup{}\mk@scripts#1_/#2% \reset@sup\mk@scripts#3_/} \makeatother % \slash \makeatletter \newbox\slashbox \setbox\slashbox=\hbox{$/$} \def\itex@pslash#1{\setbox\@tempboxa=\hbox{$#1$} \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa \copy\slashbox \kern-\@tempdima \box\@tempboxa} \def\slash{\protect\itex@pslash} \makeatother % math-mode versions of \rlap, etc % from Alexander Perlis, "A complement to \smash, \llap, and lap" % http://math.arizona.edu/~aprl/publications/mathclap/ \def\clap#1{\hbox to 0pt{\hss#1\hss}} \def\mathllap{\mathpalette\mathllapinternal} \def\mathrlap{\mathpalette\mathrlapinternal} \def\mathclap{\mathpalette\mathclapinternal} \def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}} \def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}} \def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}} % Renames \sqrt as \oldsqrt and redefine root to result in \sqrt[#1]{#2} \let\oldroot\root \def\root#1#2{\oldroot #1 \of{#2}} \renewcommand{\sqrt}[2][]{\oldroot #1 \of{#2}} % Manually declare the txfonts symbolsC font \DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n} \SetSymbolFont{symbolsC}{bold}{U}{txsyc}{bx}{n} \DeclareFontSubstitution{U}{txsyc}{m}{n} % Manually declare the stmaryrd font \DeclareSymbolFont{stmry}{U}{stmry}{m}{n} \SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n} % Manually declare the MnSymbolE font \DeclareFontFamily{OMX}{MnSymbolE}{} \DeclareSymbolFont{mnomx}{OMX}{MnSymbolE}{m}{n} \SetSymbolFont{mnomx}{bold}{OMX}{MnSymbolE}{b}{n} \DeclareFontShape{OMX}{MnSymbolE}{m}{n}{ <-6> MnSymbolE5 <6-7> MnSymbolE6 <7-8> MnSymbolE7 <8-9> MnSymbolE8 <9-10> MnSymbolE9 <10-12> MnSymbolE10 <12-> MnSymbolE12}{} % Declare specific arrows from txfonts without loading the full package \makeatletter \def\re@DeclareMathSymbol#1#2#3#4{% \let#1=\undefined \DeclareMathSymbol{#1}{#2}{#3}{#4}} \re@DeclareMathSymbol{\neArrow}{\mathrel}{symbolsC}{116} \re@DeclareMathSymbol{\neArr}{\mathrel}{symbolsC}{116} \re@DeclareMathSymbol{\seArrow}{\mathrel}{symbolsC}{117} \re@DeclareMathSymbol{\seArr}{\mathrel}{symbolsC}{117} \re@DeclareMathSymbol{\nwArrow}{\mathrel}{symbolsC}{118} \re@DeclareMathSymbol{\nwArr}{\mathrel}{symbolsC}{118} \re@DeclareMathSymbol{\swArrow}{\mathrel}{symbolsC}{119} \re@DeclareMathSymbol{\swArr}{\mathrel}{symbolsC}{119} \re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46} \re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121} \re@DeclareMathSymbol{\Vbar}{\mathrel}{symbolsC}{121} \re@DeclareMathSymbol{\sslash}{\mathrel}{stmry}{12} \re@DeclareMathSymbol{\bigsqcap}{\mathop}{stmry}{"64} \re@DeclareMathSymbol{\biginterleave}{\mathop}{stmry}{"6} \re@DeclareMathSymbol{\invamp}{\mathrel}{symbolsC}{77} \re@DeclareMathSymbol{\parr}{\mathrel}{symbolsC}{77} \makeatother % \llangle, \rrangle, \lmoustache and \rmoustache from MnSymbolE \makeatletter \def\Decl@Mn@Delim#1#2#3#4{% \if\relax\noexpand#1% \let#1\undefined \fi \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#3}{#4}} \def\Decl@Mn@Open#1#2#3{\Decl@Mn@Delim{#1}{\mathopen}{#2}{#3}} \def\Decl@Mn@Close#1#2#3{\Decl@Mn@Delim{#1}{\mathclose}{#2}{#3}} \Decl@Mn@Open{\llangle}{mnomx}{'164} \Decl@Mn@Close{\rrangle}{mnomx}{'171} \Decl@Mn@Open{\lmoustache}{mnomx}{'245} \Decl@Mn@Close{\rmoustache}{mnomx}{'244} \Decl@Mn@Open{\llbracket}{stmry}{'112} \Decl@Mn@Close{\rrbracket}{stmry}{'113} \makeatother % Widecheck \makeatletter \DeclareRobustCommand\widecheck[1]{{\mathpalette\@widecheck{#1}}} \def\@widecheck#1#2{% \setbox\z@\hbox{\m@th$#1#2$}% \setbox\tw@\hbox{\m@th$#1% \widehat{% \vrule\@width\z@\@height\ht\z@ \vrule\@height\z@\@width\wd\z@}$}% \dp\tw@-\ht\z@ \@tempdima\ht\z@ \advance\@tempdima2\ht\tw@ \divide\@tempdima\thr@@ \setbox\tw@\hbox{% \raise\@tempdima\hbox{\scalebox{1}[-1]{\lower\@tempdima\box \tw@}}}% {\ooalign{\box\tw@ \cr \box\z@}}} \makeatother % \mathraisebox{voffset}[height][depth]{something} \makeatletter \NewDocumentCommand\mathraisebox{moom}{% \IfNoValueTF{#2}{\def\@temp##1##2{\raisebox{#1}{$\m@th##1##2$}}}{% \IfNoValueTF{#3}{\def\@temp##1##2{\raisebox{#1}[#2]{$\m@th##1##2$}}% }{\def\@temp##1##2{\raisebox{#1}[#2][#3]{$\m@th##1##2$}}}}% \mathpalette\@temp{#4}} \makeatletter % udots (taken from yhmath) \makeatletter \def\udots{\mathinner{\mkern2mu\raise\p@\hbox{.} \mkern2mu\raise4\p@\hbox{.}\mkern1mu \raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}} \makeatother %% Fix array \newcommand{\itexarray}[1]{\begin{matrix}#1\end{matrix}} %% \itexnum is a noop \newcommand{\itexnum}[1]{#1} %% Renaming existing commands \newcommand{\underoverset}[3]{\underset{#1}{\overset{#2}{#3}}} \newcommand{\widevec}{\overrightarrow} \newcommand{\darr}{\downarrow} \newcommand{\nearr}{\nearrow} \newcommand{\nwarr}{\nwarrow} \newcommand{\searr}{\searrow} \newcommand{\swarr}{\swarrow} \newcommand{\curvearrowbotright}{\curvearrowright} \newcommand{\uparr}{\uparrow} \newcommand{\downuparrow}{\updownarrow} \newcommand{\duparr}{\updownarrow} \newcommand{\updarr}{\updownarrow} \newcommand{\gt}{>} \newcommand{\lt}{<} \newcommand{\map}{\mapsto} \newcommand{\embedsin}{\hookrightarrow} \newcommand{\Alpha}{A} \newcommand{\Beta}{B} \newcommand{\Zeta}{Z} \newcommand{\Eta}{H} \newcommand{\Iota}{I} \newcommand{\Kappa}{K} \newcommand{\Mu}{M} \newcommand{\Nu}{N} \newcommand{\Rho}{P} \newcommand{\Tau}{T} \newcommand{\Upsi}{\Upsilon} \newcommand{\omicron}{o} \newcommand{\lang}{\langle} \newcommand{\rang}{\rangle} \newcommand{\Union}{\bigcup} \newcommand{\Intersection}{\bigcap} \newcommand{\Oplus}{\bigoplus} \newcommand{\Otimes}{\bigotimes} \newcommand{\Wedge}{\bigwedge} \newcommand{\Vee}{\bigvee} \newcommand{\coproduct}{\coprod} \newcommand{\product}{\prod} \newcommand{\closure}{\overline} \newcommand{\integral}{\int} \newcommand{\doubleintegral}{\iint} \newcommand{\tripleintegral}{\iiint} \newcommand{\quadrupleintegral}{\iiiint} \newcommand{\conint}{\oint} \newcommand{\contourintegral}{\oint} \newcommand{\infinity}{\infty} \newcommand{\bottom}{\bot} \newcommand{\minusb}{\boxminus} \newcommand{\plusb}{\boxplus} \newcommand{\timesb}{\boxtimes} \newcommand{\intersection}{\cap} \newcommand{\union}{\cup} \newcommand{\Del}{\nabla} \newcommand{\odash}{\circleddash} \newcommand{\negspace}{\!} \newcommand{\widebar}{\overline} \newcommand{\textsize}{\normalsize} \renewcommand{\scriptsize}{\scriptstyle} \newcommand{\scriptscriptsize}{\scriptscriptstyle} \newcommand{\mathfr}{\mathfrak} \newcommand{\statusline}[2]{#2} \newcommand{\tooltip}[2]{#2} \newcommand{\toggle}[2]{#2} % Theorem Environments \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{lemma}{Lemma} \newtheorem{prop}{Proposition} \newtheorem{cor}{Corollary} \newtheorem*{utheorem}{Theorem} \newtheorem*{ulemma}{Lemma} \newtheorem*{uprop}{Proposition} \newtheorem*{ucor}{Corollary} \theoremstyle{definition} \newtheorem{defn}{Definition} \newtheorem{example}{Example} \newtheorem*{udefn}{Definition} \newtheorem*{uexample}{Example} \theoremstyle{remark} \newtheorem{remark}{Remark} \newtheorem{note}{Note} \newtheorem*{uremark}{Remark} \newtheorem*{unote}{Note} %------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------- \section*{Catriona Agg's puzzles 2018} \hypertarget{catriona_aggs_geometry_puzzles_from_2018}{}\section*{{Catriona Agg's Geometry Puzzles from 2018}}\label{catriona_aggs_geometry_puzzles_from_2018} \begin{enumerate}% \item [[two rectangles in a semi-circle]] \emph{Dec 31, 2018} [[TwoRectanglesinaSemiCircle\_small.png:pic]] \item [[divided hexagon iii]] \emph{Dec 30, 2018} [[DividedHexagonIII\_small.png:pic]] \item [[circles around a triangle]] \emph{Dec 16, 2018} [[CirclesAroundaTriangle\_small.png:pic]] \item [[rectangles stacked in a semi-circle]] \emph{Dec 12, 2018} [[RectanglesStackedinaSemiCircle\_small.png:pic]] \item [[two circles, two squares]] \emph{Dec 11, 2018} [[TwoCirclesTwoSquares\_small.png:pic]] \item [[subdivided square]] \emph{Dec 5, 2018} [[SubdividedSquare\_small.png:pic]] \item [[chords dividing a triangle into five]] \emph{Dec 3, 2018} [[ChordsDividingaTriangleintoFive\_small.png:pic]] \item [[three rectangles as a triangle]] \emph{Dec 1, 2018} [[ThreeRectanglesasaTriangle\_small.png:pic]] \item [[partitioned square]] \emph{Nov 28, 2018} [[PartitionedSquare\_small.png:pic]] \item [[two squares overlapping a semi-circle]] \emph{Nov 26, 2018} [[TwoSquaresOverlappingaSemiCircle\_small.png:pic]] \item [[five triangles in a rectangle]] \emph{Nov 25, 2018} [[FiveTrianglesinaRectangle\_small.png:pic]] \item [[nested circles and a triangle]] \emph{Nov 24, 2018} [[NestedCirclesandaTriangle\_small.png:pic]] \item [[square in a triangle in a square]] \emph{Nov 23, 2018} [[SquareinaTriangleinaSquare\_small.png:pic]] \item [[quarter circles in a rectangle]] \emph{Nov 22, 2018} [[QuarterCirclesinaRectangle\_small.png:pic]] \item [[semi-circles in a quarter circle]] \emph{Nov 21, 2018} [[SemiCirclesinaQuarterCircle\_small.png:pic]] \item [[three squares on a line]] \emph{Nov 19, 2018} [[ThreeSquaresonaLine\_small.png:pic]] \item [[nested circles and polygons]] \emph{Nov 18, 2018} [[NestedCirclesandPolygons\_small.png:pic]] \item [[semi-circle and tangents in a square]] \emph{Nov 17, 2018} [[SemiCircleandTangentsinaSquare\_small.png:pic]] \item [[equilateral triangle in a hexagon]] \emph{Nov 17, 2018} [[EquilateralTriangleinaHexagon\_small.png:pic]] \item [[three regular hexagons]] \emph{Nov 14, 2018} [[ThreeRegularHexagons\_small.png:pic]] \item [[triangles in a semi-circle]] \emph{Nov 13, 2018} [[TrianglesinaSemiCircle\_small.png:pic]] \item [[equilateral triangles in a square]] \emph{Nov 12, 2018} [[EquilateralTrianglesinaSquare\_small.png:pic]] \item [[three aligned triangles]] \emph{Nov 11, 2018} [[ThreeAlignedTriangles\_small.png:pic]] \item [[crossed hexagon]] \emph{Nov 10, 2018} [[CrossedHexagon\_small.png:pic]] \item [[square in a semi-circle in a square]] \emph{Nov 8, 2018} [[SquareinaSemiCircleinaSquare\_small.png:pic]] \item [[two equilateral triangles in a semi-circle]] \emph{Nov 7, 2018} [[TwoEquilateralTrianglesinaSemiCircle\_small.png:pic]] \item [[three squares in a circle]] \emph{Nov 5, 2018} [[ThreeSquaresinaCircle\_small.png:pic]] \item [[square in a circle in a quarter circle in a square]] \emph{Nov 4, 2018} [[SquareinaCircleinaQuarterCircleinaSquare\_small.png:pic]] \item [[triangle in a circle in a quarter circle in a square]] \emph{Nov 4, 2018} [[TriangleCircleQuarterCircleSquare\_small.png:pic]] \item [[arcs inside a triangle]] \emph{Nov 2, 2018} [[ArcsInsideaTriangle\_small.png:pic]] \item [[quadrilateral from two squares in a square]] \emph{Oct 30, 2018} [[QuadrilateralfromTwoSquaresinaSquare\_small.png:pic]] \item [[triangle centres and square corners]] \emph{Oct 29, 2018} [[TriangleCentresandSquareCorners\_small.png:pic]] \item [[hexagon and concentric circles]] \emph{Oct 28, 2018} [[HexagonandConcentricCircles\_small.png:pic]] \item [[chord and annulus]] \emph{Oct 27, 2018} [[ChordandAnnulus\_small.png:pic]] \item [[dissected hexagon]] \emph{Oct 26, 2018} [[DissectedHexagon\_small.png:pic]] \item [[circles in rhombii sequal]] \emph{Oct 26, 2018} [[CirclesinRhombiiSequal\_small.png:pic]] \item [[circles in triangle and rhombus]] \emph{Oct 25, 2018} [[CirclesinTriangleandRhombus\_small.png:pic]] \item [[circles resting on triangles]] \emph{Oct 24, 2018} [[CirclesRestingonTriangles\_small.png:pic]] \item [[arbelos]] \emph{Oct 23, 2018} [[Arbelos\_small.png:pic]] \item [[four circles in a triangle in a circle]] \emph{Oct 22, 2018} [[FourCirclesinaTriangleinaCircle\_small.png:pic]] \item [[triangles with a parallelogram]] \emph{Oct 21, 2018} [[TriangleswithaParallelogram\_small.png:pic]] \item [[three squares in a square]] \emph{Oct 18, 2018} [[ThreeSquaresinaSquare\_small.png:pic]] \item [[two circles in an equilateral triangle]] \emph{Oct 17, 2018} [[TwoCirclesinanEquilateralTriangle\_small.png:pic]] \item [[semi-circles in a square]] \emph{Oct 15, 2018} [[SemiCirclesinaSquare\_small.png:pic]] \item [[five rectangles in a square]] \emph{Oct 14, 2018} [[FiveRectanglesinaSquare\_small.png:pic]] \item [[five overlapping circles]] \emph{Oct 11, 2018} [[FiveOverlappingCircles\_small.png:pic]] \item [[four regular polygons]] \emph{Oct 8, 2018} [[FourRegularPolygons\_small.png:pic]] \item [[four squares around a quadrilateral]] \emph{Oct 7, 2018} [[FourSquaresAroundaQuadrilateral\_small.png:pic]] \item [[two perpendicular equilateral triangles]] \emph{Oct 6, 2018} [[TwoPerpendicularEquilateralTriangles\_small.png:pic]] \item [[nested circles and polygons ii]] \emph{Oct 5, 2018} [[NestedCirclesandPolygonsII\_small.png:pic]] \item [[spiralling semi-circles]] \emph{Oct 3, 2018} [[SpirallingSemiCircles\_small.png:pic]] \item [[five decreasing squares]] \emph{Oct 1, 2018} [[FiveDecreasingSquares\_small.png:pic]] \item [[triangle and semi-circle in a circle]] \emph{Sep 29, 2018} [[TriangleandSemiCircleinaCircle\_small.png:pic]] \item [[subdivided parallelogram]] \emph{Sep 27, 2018} [[SubdividedParallelogram\_small.png:pic]] \item [[triangle in four rectangles]] \emph{Sep 26, 2018} [[TriangleinFourRectangles\_small.png:pic]] \item [[circle in a trapezium]] \emph{Sep 24, 2018} [[CircleinaTrapezium\_small.png:pic]] \item [[subdivided triangle]] \emph{Sep 19, 2018} [[SubdividedTriangle\_small.png:pic]] \item [[two circles inside a square]] \emph{Sep 17, 2018} [[TwoCirclesInsideaSquare\_small.png:pic]] \item [[concentric semi-circles]] \emph{Sep 16, 2018} [[ConcentricSemiCircles\_small.png:pic]] \item [[shaded spikes in a hexagon]] \emph{Sep 14, 2018} [[ShadedSpikesinaHexagon\_small.png:pic]] \item [[squares in an octagon]] \emph{Sep 11, 2018} [[SquaresinanOctagon\_small.png:pic]] \item [[four squares in a big square]] \emph{Sep 9, 2018} [[FourSquaresinaBigSquare\_small.png:pic]] \item [[stacked boxes in circles in squares]] \emph{Sep 8, 2018} [[StackedBoxesinCirclesinSquares\_small.png:pic]] \item [[four stacked squares in a circle in a square]] \emph{Sep 8, 2018} [[FourStackedSquaresinaCircleinaSquare\_small.png:pic]] \item [[overlapping square and circle]] \emph{Sep 6, 2018} [[OverlappingSquareandCircle\_small.png:pic]] \item [[two circles inscribed in triangles in a semi-circle]] \emph{Sep 3, 2018} [[TwoCirclesInscribedinTrianglesinaSemiCircle\_small.png:pic]] \item [[arcs in a circle]] \emph{Sep 1, 2018} [[ArcsinaCircle\_small.png:pic]] \item [[six squares in a hexagon]] \emph{Aug 31, 2018} [[SixSquaresinaHexagon\_small.png:pic]] \item [[four equilateral triangles round a square]] \emph{Aug 30, 2018} [[FourEquilateralTranglesRoundaSquare\_small.png:pic]] \item [[two triangles in a rectangle]] \emph{Aug 29, 2018} [[TwoTrianglesinaRectangle\_small.png:pic]] \item [[two overlapping squares iii]] \emph{Aug 28, 2018} [[TwoOverlappingSquaresIII\_small.png:pic]] \item [[two isosceles triangles]] \emph{Aug 28, 2018} [[TwoIsoscelesTriangles\_small.png:pic]] \item [[four isosceles triangles in a circle]] \emph{Aug 26, 2018} [[FourIsoscelesTrianglesinaCircle\_small.png:pic]] \item [[two octagons and two squares]] \emph{Aug 25, 2018} [[TwoOctagonsandTwoSquares\_small.png:pic]] \item [[hexagon in a star in a hexagon]] \emph{Aug 24, 2018} [[HexagoninaStarinaHexagon\_small.png:pic]] \item [[stacked hexagons]] \emph{Aug 23, 2018} [[StackedHexagons\_small.png:pic]] \item [[a square, triangle, and circle in a square]] \emph{Aug 22, 2018} [[ASquareTriangleandCircleinaSquare\_small.png:pic]] \item [[region of an octagon]] \emph{Aug 21, 2018} [[RegionofanOctagon\_small.png:pic]] \item [[semi-circle in a square]] \emph{Aug 20, 2018} [[SemiCircleinaSquare\_small.png:pic]] \item [[polygons with equal perimeter]] \emph{Aug 19, 2018} [[PolygonswithEqualPerimeter\_small.png:pic]] \item [[stacked shapes]] \emph{Aug 19, 2018} [[StackedShapes\_small.png:pic]] \item [[four squares overlapping a circle]] \emph{Aug 17, 2018} [[FourSquaresOverlappingaCircle\_small.png:pic]] \item [[triangle in circle in triangle in semi-circle]] \emph{Aug 15, 2018} [[TriangleinCircleinTriangleinSemiCircle\_small.png:pic]] \item [[bell-ringing braids]] \emph{Aug 14, 2018} [[BellRingingBraids\_small.png:pic]] \item [[four equilateral triangles]] \emph{Aug 13, 2018} [[FourEquilateralTriangles\_small.jpg:pic]] \item [[three squares and two equilateral triangles]] \emph{Aug 13, 2018} [[ThreeSquaresandTwoEquilateralTriangles\_small.png:pic]] \item [[zig-zag triangles]] \emph{Aug 12, 2018} [[ZigzagTriangles\_small.png:pic]] \item [[squares meeting in a circle]] \emph{Aug 12, 2018} [[SquaresMeetinginaCircle\_small.png:pic]] \item [[four aligned squares]] \emph{Aug 10, 2018} [[FourAlignedSquares\_small.png:pic]] \item [[three aligned squares]] \emph{Aug 9, 2018} [[ThreeAlignedSquares\_small.png:pic]] \item [[lengths in a crossed trapezium]] \emph{Aug 9, 2018} [[LengthsinaCrossedTrapezium\_small.png:pic]] \item [[overlapping squares]] \emph{Aug 8, 2018} [[OverlappingSquares\_small.png:pic]] \item [[toppled square]] \emph{Aug 7, 2018} [[ToppledSquare\_small.png:pic]] \item [[two rectangles overlapping a circle]] \emph{Aug 2, 2018} [[TwoRectanglesOverlappingaCircle\_small.png:pic]] \item [[subdivided circles]] \emph{May 21, 2018} [[SubdividedCircles\_small.png:pic]] \end{enumerate} \end{document}