- Englishthe golden ratio (and aphrodite's phi)function - tangent - derivativesinscribed quadrilateralsthe exponential and the logarithmic functionsthe quadratic function-1ptolemy's theoremsfind the function (sine curves)find the functionfunction and derivatives-9function and derivatives-8function and derivatives-7function and derivatives-6function and derivatives-5vectors - a no word introductionfind the slopefunction and derivatives-4equilateral triangle (SAS)a family of linesgraph the linea math trick-3minimum areafind the equation of the linefunction and derivatives-3function and derivatives-2function and derivatives-1measuring van gogh's cypressareas of similar trianglesa math trick-1median to the hypotenusea math trick-2square vs rhombuspythagorean theorem (proof)eight curvereflections-4rose curvescardioidinvolute of a circlereflections-3hyperbolic spiralcochleoidlituusfermat's spiralpythagorean spiralreflections-2maximum volumeminimum perimeterareas inside a parallelogramareas inside a trapezoidpythagorean and galileo's lawarchimedes' spiralthe logarithmic spiralpower of a pointarea between a curve and x-axisarea between two curvesthe lunes of Alhazenarchimedes' arbelosFibonacci spiralVectors_1vectors_2a translation of y=-2x^2triangle midpoint theoremthe triangle inequalitya translation of the curve y=-1/xthe locus of the intersection of two linesthe angle bisector theoremsthe lune of Hippocratesa hyperbola (equation)conjugate hyperbolaspoint symmetrythe reflective property of hyperbolathe reflective property of ellipsethe reflective property of parabolaclassifying triangles...the distance between two pointsan ellipse (equation)exploring sine curvesa parabola (equation)a circle (equation)midpoint parallelograma decagonthe intersept (thales) theorema function...double reflectionGarfield's proof for pythagorean theoremtriangles...tangent at a pointthe graphs of trigonometric functionstangent lines to a circleregular octagonangle bisectorThales' theoremtangent-chord angletriangle angle-sum theoremsquare roots in a greek way...angles between parallels...y=mx+bmeasuring angles...trig values of any angleequation of a linereflections...a proof of pythagorean theorem-4pythagorean theorem (a puzzle)geometric constructions - 12geometric constructions - 132x2 linear system (Cramer's rule)an identity...moving a parabolageometric constructions - 11geometric constructions - 2area of a kiteunit circle definition of trig functionsarea of a parallelograma proof of pythagorean theoremarea of a trianglearea of a trapezoidarea of a rectangle2x2 linear system-1a pyramid inside a cube...tux walks up and down...a prism inside a prism...the line: ax+by=capproximating piconstructing a hyperbola...constructing a parabolaconstructing an ellipse...the quadratic functionadding integers...locating reals on a number linea triangleangles in a circle...measurements in a circlemodern teacherthe relative position of two circlesa cube...regular tetrahedroncube3dfive roseshexagonal prismsquare pyramidthe outer Napoleon trianglea pyramid inside a cube-1reflections of a triangleequation of a line (A, m)equation of a line (A, B)equation of a line (linear form)the golden ratioa testmakertranslations of f(x)=|x|central and inscribed anglestranslations of f(x)=x^2translations of f(x)=sqrt(x)even or odd?Vieta's formulassierpinski trianglestranslations of f(x)=1/xfind the areaquadratic formulacartesian systemthe graph of a functionregular polygonsan identity-2triangle-1right triangle trigonometry-1area of a rectangle-1the linear functionsimson linenine-point circleangle bisector as locusincircle and excircles of a triangleregular polygons-1an archimedes' formulaarea of a circlearea of a circle-1radiansproperties of a rhombusproperties of a rectangleproperties of a trapezoidproperties of a parallelogramproperties of a squareaxis of symmetrypoint of symmetryfind the tan(φ)solve the equationequal chordsproperties of an isosceles trapezoidan isosceles triangle...properties of a kitecuboidf(x)=a|x-b|+ca tank with a tapabsolute value inequalitiescomponents of a forcef(x)=a/(x-b)+cf(x)=mx+bfind the anglesf(x)=ax^2+bx+cfind the anglef(x)=atan(b(x-c))+dan equilateral triangleperpendicular linesf(x)=a^x, g(x)=log_a(x)the addition law of probabilityright triangle trigonometry-2sum of the interior angles of a n-gona Reuleaux trianglecongruent trianglesminimum area (line)maximum area (angle)adding and subtracting integersthe complex planeadding complex numberslinear transformations-1linear transformations-2area of an equilateral trianglethe witch of agnesithe cissoid of dioclesdeltoidastroidnephroidranunculoidconchoid of nicomedeslimacon of pascalcycloidstrammel of archimedesgeneralization (pappus) of pythagoreanconchoid of a circlepiriformratio of areas-1ratio of areas-2coordinates-1 (reflection)coordinates-2 (distance)equilateral hyperboladivision of a segmentan apollonian circleparabolasellipseshyperbolasa definition of conics (directrix)ellipse as a hypotrochoidellipses and hyperbolaseight curve (construction)coordinates of midpointf(x)=sinx/xradical axis-1radical axis-2law of sines (proof)law of cosines (proof)tangent and derivativef(x)=xsin(1/x)archimedes' twin circlesroots of the quadratic equationf(x)=(cosx-1)/xf(x)=e^x/xf(x)=lnx/xf(x)=xlnx-x+carchimedes' "salinon"the flower of lifethe seed of lifeyin-yangdiagonals of n-gonsJohnson's theoremKoch snowflakeconstruction of a triangle (sss)miquel's triangle theoremproof of pythagorean-5Kaleidoscopethe three squares problemhippias' quadratrixangle trisectionfirst brocard pointnagel pointgergonne pointx/a+y/b=1collinear points-1collinear points-2morley's trianglerolling circle squares itselfgeometric-arithmetic mean inequalitydistance between point-linenapier's inequalitylaw of cosines (pww)vivianni's theoremaristarchus' inequalitiesx+1/xthm about right triangleschords and tangentsregular star polygonssquaring a rectanglepitot theoremcolorsf(x)=|αx^2+bx+c|f(x)=ax^4+bx^2+cquadratic function in any formangle between secantsthe common tangent of two parabolasparallel tangents of an ellipsea property of the hyperbolathe center of an intervalabsolute valuetangents to a circleregular pentagona clocka clock(2)five squaresgolden ratio-3golden trianglegolden rectanglethe famous "1/7" trianglethe famous "1/5" squareequal chords-1supplementary anglesf(x)=asin(b(x-c))+df(x)=acos(b(x-c))+dcoordinates of a vectoraristotle's wheel paradoxparallel chords theoremsimilar ellipseseccentricity of an ellipsecoordinates-3 (reflection)from kite to rhombus and squarechord theoremsecant-secant theoremtangent-secant theoremtrigonometry_unit circlefractions in a greek way...the mean value theoremareas-3area of a triangle (sas)area of a quadrilateralarea of a triangle-2Brahmagupta's formulaarea of an ellipsea square in a squarean extrema problem-1an extrema problem-2lemoine pointexeter pointpyth-proofpyth-proof7a butterfly curvedevil's curvesparametric ellipsetrifoliumparametric hyperbolacircle and ellipsebifoliumfish curvedevil's curves-1devil's curves-2kappacurveright strophoidparallel tangents of an ellipse-1find LCM and GCDf(x)=ax^nf(x)=x^qfoliumtorpedo curveconstructing a trifoliumtrifolium-1bicorntrisectrix of maclaurindeltoidastroidversorialimacon of pascal-1cardioid-1cissoid of diokleslemniscate of bernoullieightcurveconchoid of nicomedes-1ellipse-1circle-1hyperbola-1parabola-1inverse of f(x)=mx+binverse of f(x)=q+sqrt(a(x-p))f(x)=q+sqrt(r^2-(x-p)^2)inverse of f(x)=q+a(x-p)^3quadrilaterals-2inverse of f(x)=q+a^(x-p)basic trig numbers-2basic trig numbers-1f(x)=psinx+qcosxdot productan extrema problem-3polar form of a complexthe nth roots of unityrolling coin paradoxvecten pointsfeuerbach's pointarc length (verification)pythagorean (verification)right triangle paradoxsquare-rectangle paradoxisosceles triangle paradoxsphere in cylindercone in cylinderall the linestangent-chord angle-1inscribed angles-1tangent to a circlean extrema problem-4an extrema problem-5pentalphastar of davidproperties of the altitudescommon external tangentscommon internal tangentscommon external tangents-1common internal tangents-1geometric mean theoremfrustum of a right conefrustum of a regular pyramidcylinder in conea butterfly curve-1convex quadrilateralsapproximating pi-12x2 linear systema clock-3find the area-1square numberstriangular numberstriangular numbers-1pythagorean triples-euclidpythagorean triples-platopythagorean triples-proclusproof of pythagorean-9euclid's proof of pythagoreanmultiplicative inverse of a complexdevil's curves-3circles of a regular n-gonthe bell curvepascal's trianglea multiplication tableabsolute value inequalities2absolute value inequalities1Area of Circles (3)Shading Venn Diagrams (1)equations and problemspendulumRolling Coin 滾動的硬幣 (1)Solving Similar Triangles (1)fractional exponentsThe Sum of the First n Natural Numbers - Dynamic Proofangles between parallels-1Practicing Statistical Calculation-1pie chartdistribution of lettersSum of the CubeshistogramsWater Trianglemeasures of centerpi digitsmake an anglelinear systemfrequency scaleSeven Circles Theoremcircumference of circles-1tangram puzzle-1multiplication table-1fraction αdditioncoin flipping-1flipping 5 coinsflipping a coinevaluating logarithms practicefraction division: a ÷ b (partitive)fraction multiplicationcomparing fractionssubtraction of proper fractionsbinomial and normalrandom data-1random data-2coin tossing simulationnewton's cradledotplotrussian multiplicationa math trick-31cube of a binomialbinomial distributioncylinder in a coneabsolute value inequalities-testgraph the line-1a wheel of fortuneferris wheelwheel of fortune-1the reuleaux triangle-1newton's diskintegrationa wheel of fortune-1fraction to decimalpoints and segmentsbinomial formuladifference of two squaresconway circletangent and derivativeparallels or not?lines through a pointrolling two dice-1rolling a diceegyptian system of numerationrolling two diceregular polygons-3Fahrenheit to Celsiusthe sum of the first n oddsieve of eratosthenesmoon and seadecimal and binary systemstemperaturestring artthe height of the pyramid
