This page is for animated GIFs as well as (cropped) PDF pictures and the $latex \LaTeX$ code that created it.

Basic Shapes (Graphs every high school student should know)


$latex y = x$          BasicShape1 (.tex file)             BasicShape1 (cropped PDF)

$latex y = x^2$         BasicShape2 (.tex file)            BasicShape2 (cropped PDF)

$latex y = x^3$         BasicShape3  (.tex file)           BasicShape3  (cropped PDF)

XeLatex or $latex \LaTeX$

$latex y = \sqrt x$       BasicShape4  (.tex file)          BasicShape4   (cropped PDF)

$latex y=\frac{1}{x}$          BasicShape5   (.tex file)        BasicShape5   (cropped PDF)

$latex y=|x|$          BasicShape6  (.tex file)           BasicShape6   (cropped PDF)

$latex y=\lceil x \rceil$        BasicShape7  (.tex file)        BasicShape7   (cropped PDF)

$latex y=\lfloor x \rfloor$     BasicShape8  (.tex file)        BasicShape8   (cropped PDF)

$latex y=\sin(x)$     BasicShape9   (.tex file)        BasicShape9   (cropped PDF)

$latex y=\cos(x)$    BasicShape10  (.tex file)       BasicShape10   (cropped PDF)

$latex y=\tan(x)$   BasicShape11   (.tex file)     BasicShape11   (cropped PDF)

$latex y=\tan(x)$ [asymptotes] BasicShape11B (.tex file) BasicShape11B (cropped PDF)

$latex y=a^{x} \mbox{ if } (a>1)$  BasicShape12  (.tex file)  BasicShape12  (cropped PDF)

$latex y=a^{-x} \mbox{ if } (a>1)$   BasicShape13  (.tex file)   BasicShape13  (cropped PDF)

$latex y=e^{x}$   BasicShape14  (.tex file)  BasicShape14  (cropped PDF)

$latex y=\log_a(x)$   BasicShape15  (.tex file)   BasicShape15  (cropped PDF)

$latex y=\ln(x)$  BasicShape16  (.tex file)   BasicShape16  (cropped PDF)

$latex y=e^{-x}$  BasicShape17  (.tex file)   BasicShape17  (cropped PDF)

$latex y=\arccos(x)$  arccos (.tex file)  arccos (cropped PDF)

$latex y=\arcsin(x)$  arcsin (.tex file)  arcsin (cropped PDF)

$latex y=\arctan(x)$  arctan (.tex file)  arctan (cropped PDF)

restricted sine    ressine   (.tex file)   ressine  (cropped PDF)

restricted cosine   rescos  (.tex file)  rescos  (cropped PDF)

restricted tangent   restan   (.tex file)  restan   (cropped PDF)

Reference Triangles

45-45-90 (radians) RefTri (.tex)  RefTri (PDF)

30-60-90 (radians)  RefTriB (.tex)  RefTriB (PDF)

45-45-90 (degrees)  RefTriDeg (.tex)  RefTriDeg (PDF)

30-60-90 (degrees)  RefTriBDeg (.tex)  RefTriBDeg (PDF)

Polygons Inscribed in Circles:  Poly3InscPoly4InscPentInscPoly6InscPoly8Insc,  Poly10InscPoly20Insc (PDF files) LaTeX files: PentInscPoly20Insc

Circles Inscribed in Polygons: CircInscr (.tex) CircInscr3CircInscr4CircInscr5CircInscr6CircInscr8CircInscr10 (cropped PDF)


Sierpinski's Triangle (created with Sage): 1 iteration: sierpinski1, 2 iterations: sierpinski2, 3 iterations: sierpinski3, 4 iterations: sierpinski4, 5 iterations: sierpinski5, 6 iterations: sierpinski6, 7 iterations: sierpinski7, 8 iterations: sierpinski8, 9 iterations: sierpinski9

Sierpinski's Carpet (created with Sage): 1 iteration: SC1, 2 iterations: SC2, 3 iterations: SC3, 4 iterations: SC4, 5 iterations: SC5, 6 iterations: SC6

Koch Snowflake (created with Sage): 0 iterations: KochSnowflake0, 1 iteration KochSnowflake1, 2 iterations: KochSnowflake2, 3 iterations: KochSnowflake3, 4 iterations: KochSnowflake4, 5 iterations: KochSnowflake5

Fractal Fern (created with Sage): FractalFern1000 (1000 points), FractalFern10K (10,000 points), FractalFern40000 (40,000 points)

Pythagorean Tree (created with Sage): Balanced: PythagoreanTree1PythagoreanTree2PythagoreanTree3PythagoreanTree4,


PythagoreanTree9PythagoreanTree10 Unbalanced: PythagoreanTreeB1PythagoreanTreeB2,


Thales' Theorem 1: Thales (.tex)  Thales (cropped PDF) Thales1 (.tex) Thales1 ( cropped PDF)

Thales' Theorem 2: Thales2 (.tex)  Thales2 (PDF)

An Important Limit: LimSin (.tex) LimSin (PDF)     LimSin2 (.tex)  LimSin2 (PDF)

3D Solids:

Rectangular prism: RecPrism  (.tex)  RecPrism (PDF)    Cone: Cone (.tex) Cone (PDF)

Pyramid: Pyramid (.tex)   Pyramid (PDF)                 Sphere: Sphere (.tex)  Sphere (PDF)

Cylinder: Cylinder (.tex)   Cylinder (PDF)                           Cube: Cube (.tex)  Cube (PDF)         

 Pythagorean Theorem diagram: PythTh (.tex) PythTh (PDF)

Japanese Line Functions (Amidakuji)JapLineFcnDiag1 (.tex) JapLineFcnDiag1 (PDF) JapLineFcnDiag2 (.tex) JapLineFcnDiag2 (PDF)  JapLineFcnDiag3 (.tex) JapLineFcnDiag3 (PDF) JapLineFcnDiag4 (.tex) JapLineFcnDiag4 (PDF)

Amidakuji points diagram: JapLineFcnPointsDiag (.tex) JapLineFcnPointsDiag (PDF)

Pythagorean Theorem Converse diagram: PythConvDiag (.tex)  PythConvDiag (PDF)

3D distance using Pythagorean Theorem: Pyth3D (.tex) Pyth3D (PDF)

Area under $latex y=x^2$ with upper and lower Riemann sums:   Intx2Region (tex) Intx2Region (PDF)   Intx2Low (tex)  Intx2Low (PDF)   Intx2Up (tex)  Intx2Up (PDF)

Area under $latex y=x^2$ with 25 rectangles without/with magnifying glass: Intx2Up25 (tex) Intx2Up25 (PDF)   Intx2Up25Spy (tex)  Intx2Up25Spy (PDF)

Paint Can Curve: PaintFunc (tex)  PaintFunc (PDF)

H-Trees (PDF files): H-Tree1iteration   H-Tree2iterations   H-Tree3iterations  H-Tree4iterations  H-Tree-5iterations   H-Tree6iterations  H-Tree with varying thicknesses: H-Tree6V

Area of Circle (PDF): AreaOfCircle4   AreaOfCircle6   AreaOfCircle8   AreaOfCircle10   AreaOfCircle12  AreaOfCircle14  AreaOfCircle40

Prime Function (PDF): primefunction

Acute/obtuse triangles for Law of Sines/Cosines: AcuteTri (tex)  AcuteTriB (tex)  ObtuseTri (tex)  ObtuseTriB (tex)  AcuteTri (PDF)  AcuteTriB (PDF)  ObtuseTri (PDF)  ObtuseTriB (PDF)

Newton's Method (chaos): EACH FILE IS 10 MB  NewtonsMethod250_5_7 (PDF) NewtonsMethod250_5_8 (PDF)

Dragon Curve: DragonCurve12  (PDF) DragonCurve18iter (PDF)

Law Of Sines: Ambiguous Case (cropped PDF)  AmbigCaseA1 (.tex)  AmbigCaseA1 (PDF) AmbigCaseA2 (.tex) AmbigCaseA2 (PDF)  AmbigCaseA3 (.tex)  AmbigCaseA3 (PDF) AmbigCaseA3a (.tex) AmbigCaseA3a (PDF)  AmbigCaseA4 (.tex)  AmbigCaseA4 (PDF) AmbigCaseA4a (.tex)  AmbigCaseA4a (PDF)  AmbigCaseO1 (.tex)  AmbigCaseO1 (PDF)  AmbigCaseO2 (.tex)  AmbigCaseO2  (PDF)  AmbigCaseO2a (.tex)  AmbigCaseO2a (PDF)

Riemann Sums: Riem1L2   Riem1L3   Riem1L4   Riem1L10  Riem1L100  Riem1U2  Riem1U3  Riem1U4  Riem1U10  Riem1U100  (PDFs) Riem1 (.tex)

Hyperbolas: HyperbVert  (tex)   HyperbV (PDF)  HyperbolaHor  (tex)HyperbH  (PDF)  HyperbHorUnlabeled  (tex)  HyperbHUnlabeled  (PDF)

Discontinuity: Discont1  (PDF) Discont2  (PDF)  Discont3  (PDF)  Limit4   (PDF)

Differentiable at 0: SinIx2sin  (PDF)  Graph of Derivative: DSinIx2sin  (PDF)

Flow Chart: FlowChart  (.tex)  FlowChart  (PDF)

Random Bipartite Graph: RandBi   (tex) Sample (random) output: RandBi  (PDF)

Relationship between $latex \lceil x \rceil$ and $latex \lfloor x \rfloor$ FloorCeiling (PDF)

Dartboard (3 rings)  Dartboard1 (tex)  Dartboard1 (PDF)  (4 rings)  Dartboard2    (tex) Dartboard2    (PDF)

Dice:   Dice1  (PDF)  Dice2  (PDF)

Menger Sponge: Menger1  (PDF)   Menger2  (PDF)  Menger3  (PDF)   Menger4   (PDF)

Rock, Paper, Scissors, Lizard, Spock: RPSLS (.tex)  RPSLS  (PDF)

TI-84 plus graphing calculator: GraphCalculator   (PDF)

List the Rationals: ListRationals  (.tex)  ListRationals  (PDF)

Hyperbolic Trig Functions: sinh (PDF) cosh (PDF) tanh (PDF) csch (PDF)  sech (PDF)  coth (PDF)

Linearization of $latex \sqrt{x}$:  SqrtSpy1  (PDF)

Arc Length: ArcLength  (PDF)

Snell's Law (see here for details)SnellsLaw1 (PDF)  SnellsLaw2 (PDF)

Exponential and Logarithm: ExpLog  [ growth](PDF)   ExpLogD  [decay] (PDF)

Piecewise functions: Piecewise1Piecewise2 ,  Piecewise3Piecewise4  (PDFs)   Piecewise1  (.tex)

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