Files On Big C Website

File Name To open, click on either the *name* or the *icon* below:	Description of files are in this column. The URL of this page is: http://www.bigcsociety.org/dan/TheGeometersSketchpad.html My E-Mail Address is: danlufkin@calalum.org (Dan Lufkin)
1. Original Introduction	My first 'introductory' sketch first used at a 'SUG' (Sketchpad User's Group) presentation at a national NCTM conference in San Diego, CA
2. Masses Evangel	The first part of this sketch shows me, the 'evangelist' riding in on the wings of an angel (OK, a falcon!) spreading the 'Gospel' of Sketchpad. The remainder of the sketch demonstrates the construction of the 4 centers of a triangle. Centroid CircumCenter OrthoCenter InCenter
3. Belt Around The Earth	The 'Belt Around the Earth' problem has intrigued me ever since I became aware of it. In the beginning, I was only able to use 'manipulatives' (string, beach ball). With the creation of *The Geometer's Sketchpad* , the results are even more impressive! Accompanying the sketches is a simple algebraic proof of the results.
4. Fibonacci	The Fibonacci sequence is quite remarkable. Books (and full college courses) exist just to present/explain it. It has become even more 'fashionable' with the appearance of 'The Da Vinci Code'. This sketch presents a 'paradox' involving squares, rectangles, congruent right triangles and trapezoids and, of course, the Fibonacci Numbers.
5. e Pi Phi	There is a Golden Rectangle. Is there a 'Golden Triangle' ? Consider the lengths of the following numbers: 'e', 'pi', and 'PHI' (the Golden Ratio). What are the characteristics of a triangle with these lengths as sides? Does it bear any relationship to the Golden Rectangle ? Why is a "3 x 5" card so important ?? Similarly, what are the characteristics of a "5 x 8" card ??
6. Law Of Cosines	A very clever way of demonstrating the Law of Cosines using a square and some 'slicing', 'dicing', and 'sliding' with *The Geometer's Sketchpad*
7. The 'Point' Game	An adaptation from 'Exploring Algebra with the Geometer's Sketchpad' (from Key Curriculum Press). Object is to match points with corresponding coordinates after a random shuffling/moving of points. A good utilization of parametric colorization.
8. The 'Panda' Joke	A break from all this action! Joke based upon book entitled: *"Eats, Shoots, and Leaves"* by Lynne Truss
9. 'Spinning' Basketball	Spinning Basketball Instructions on how to create!! However, 90% of the credit is due to Yao Liu (liuyao@gmail.com) of Key Curriculum Press. File is large (18 M) due to graphics; may take some time to load.
10. Orthocenter	The Incenter, Circumcenter, and Centroid all seem to have a 'function' in life. Does the Orthocenter ? The OrthoCenter appears to be the "Rodney Dangerfield" of the circle centers. Does the lack of respect accorded this center have any merit ? Do we need this center ? This sketch illustrates that the OrthoCenter does have a function, although somewhat esoteric.
11. Definition of a Radian.	*The Geometer's Sketchpad* looks at the 'Radian' concept from a variety of "angles" (pun intended).
12. Conics by Definition	The Four Conics depicted by their geometric definitions.
13. Triangle Morph	A paradoxical increase in area as a result of a triangle morphing.
14. One Weighing? (impossible?)	An animated problem involving 'weighing' but with only ONE weighing.
15. Dynamic Linear Equation Solving	Solving linear equations by manipulating 'sliders'
16. Pre-Made Sketch	Many people have already created *Sketchpad* sketches which you can use without knowing much about *Sketchpad*. If you click on 'Display', you will see that much thought went into the preparation of this sketch!
17. The 'Slope' Game	An adaptation from 'Exploring Algebra with the Geometer's Sketchpad' (from Key Curriculum Press). Object is to match numerical slope values with corresponding lines (segments) after a random shuffling/moving of the lines. Another good utilization of parametric colorization
18. Sinusoid & Inverse	The 'General' Sinusoid and its inverse. Total control over each of the four parameters in aSIN [b(x-h)] + k
19. GSP as a Word Processor?	Find yourself cutting and pasting between Microsoft Word and *The Geometer's Sketchpad* ? Look at all the 'Math Type/Word' features within *The Geometer's Sketchpad*.
20. y equals x-squared	An interesting look at a specific property of y equals x-squared.
21. A Look at the Least Squares Method	A very visual approach to just what is happening when one uses the the 'Least Squares' technique
22. Kaleidoscope	A Kaleidoscope fashioned after the cover on a Mathematics Teacher magazine.
23. Kaleidoscope part 2	An extension of the previous problem, including step-by-step procedures on how to make a colorful kaleidoscope.
24. Exponential Growth and Decay	*The Geometer's Sketchpad's* rendering of exponential growth and decay.
25. Linear Programming	Linear Programming Techniques
26. Halloween Party	A student's rendition of a Halloween party announcement.
27. Negative Times a Negative?	Why does a negative times a negative equal a positive ?
28. Vector Usage	Translation of functions using vectors.
29. Reuleaux Triangle	*The Geometer's Sketchpad* looks at the Reuleaux Triangle.
30. Icosahedron	A Japanese Mathematics Professor's Icosahedron
31. HyperCube	One of Nicholas Jackiw's [The Creator of Sketchpad ] first sketches
32. The Sierpinski Triangle	The Sierpinski Triangle
33. DynaDemos	A unique way of both introducing and looking at the concept of function and composition of functions.
34. Triangle Angle Sum	This is the sketch I would have liked to have had available to me in 1982 ! I think it truly exhibits the power of *The Geometer's Sketchpad* to illustrate a simple, yet important concept. It is also a very good sketch to demonstrate to others just what *The Geometer's Sketchpad* can do.
35. Plotting a Point in 3D	Plotting a point in 3-Dimensions with accompanying "box" for perspective
36. Arithmetic/Geometric Sequences	A visual approach to Arithmetic and Geometric Sequences
37. Ceva's Theorem	Ceva's Theorem...but not the way he approached it.
38. Frustrum of a Cone	A dynamic rendition of the Frustrum of a Cone
39. 'GASP' and The Da Vinci Code	Using *The Geometer's Sketchpad* to solve anagrams in The Da Vinci Code
40. A 'family' of circles!	Mom, Pop, and baby bubble stick together
41. Five Adjustable Quads	A Square, A Rectangle, A Parallelogram, A Rhombus, and A Trapezoid
42. Center of Circle	Find the center of a circle, given only an arc of the circle
43. Matrix Rotation	Rotate a point through 90, 180, and 270 degrees using matrices
44. Moire Effect	Two sets of concentric circles merging to form a Moire effect.
45. The Euler Line	The Euler Line: how it looks in 5 different triangles and the PROOF!!
46. Parametric Color Demo	A demonstration of how to create 'parametric colorization' in a sketchpad file using a hexagonal prism with a adjustable height, side length, and rotation.
47. "Slider Savvy"	How to make a Sketchpad 'slider'...and an application
48. Rhombus Constructions	There are many ways a rhombus can be constructed using its properties. Here are some of them.
49. Dynamic Graphing	Plot a function, change domain, and change scale...all in one sketch !!
50. Square Inside A Semi-Circle	See how to construct a dynamic square within a semi-circle
51. Slider: How to Construct	How to construct a 'Slider'in two different ways.
52. A "People" Ferris Wheel	A Ferris Wheel of Students!!
53. Merging Text	See a little known way of merging variable values into text expressions. For example, attaching the values of a, b, and c into the quadratic equation.
54. Piece-wise Plotting	A graphing template where you can adjust the scale, domain, and the "breakpoint" (right endpoint of 1st [left-most] function's domain) for two functions.
55. Power Point & Sketchpad	You *can* combine *The Geometer's Sketchpad* and a Power Point Presentation !
56. Perpendicular Optical Illusion	Which line segments are perpendicular to one another ??
57. Optical Illusions	How many "forks" are there? The Impossible Triangle ...and more optical illusions to come !! Send me yours to post !!
58. Segment "Lengths"	Which is longer ?? The Red Segment or the Blue Segment
59. Nametag Maker	Sketchpad can be used to make Name Tags ??
60. Ferris Wheel	Check out this wonderful Ferris Wheel !! It includes many features of Sketchpad:imported graphics, graphics overlays, background colors, multiple motions, good use of color. This was done by one of my DoD (Department of Defense) Online students, David Craig . He currently teaches at Wiesbaden American High School, Wiesbaden, Germany. He is married and has a 6-year old daughter who thinks "math is fun".
61. Inequality Solving	Inequality Graphing !! solved by The Geometer's Sketchpad. This sketch contains 'tools' that allow one to graph 8 different kinds of inequalites: y > f(x), y < f(x), y >= f(x), y <= f(x) (and 4 more 'inverse' functions). This sketch comes from 'Teaching Algebra One with The Geometer's Sketchpad' [Key Curriculum Press]
62. Week One	Week One Project !! A sketch to illustrate the concept of slope. This sketch comes from 'Teaching Algebra One with The Geometer's Sketchpad' [Key Curriculum Press]
63. Cartoon Math	"Cartoon Math" !! [From the Sunday comics section] A cartoon containing a math problem. This is an illustration of how a graphic can be copied into a sketch and, if desired, inserted in such a manner that its size can be adjustable.
64. "Hell's Angles "	"Hells Angles" !! [A "Bizzaro" cartoon] Another cartoon depicting three of the "Hell's Angles" (Right, Obtuse, and Acute. Tough-looking dudes !!
65. "Greatest Integer Function"	The "Greatest Integer Function" !! Trigonometric Functions built into Sketchpad include: Sine, Cosine, Tangent, ArcSine, ArcCosine, and ArcTangent. Other functions are: Absolute Value, Square Root, both the Logarithm functions (natural and base 10), the Signum, Round, and Truncate functions. If you have ever programmed before, you no doubt found 'The Greatest Integer Function' useful. Here it is !! [I show you how to create it; to use it, click on 'Custom Tool' icon.]
66. One Hundred Pennies	"One Hundred Pennies !!" The original problem statement, as formulated by Marilyn Vos Savant [Sunday, 21 October 2007] was as follows: "One Hundred pennies are on a table. Ten are tails. With your eyes closed, can you separate them into two groups so that each group has the same number of tails?"
67. Euler's Equation	"Euler's Equation" Euler's Equation, from a geometric point of view [This sketch has been a long time in the making!!...inspiration provided by Scott Steketee, Key Curriculum Press] The first part of the sketch demonstrates how to multiply complex numbers. The second part looks at limits. Finally, parts 1 and 2 are linked to show (geometrically) Leonhard Euler's "Most Beautiful Equation"
68. GoldiLOCs	"GoldiLOCs" Peter Gerrodette [ Peter Gerrodette...Teach4sumfun ] created these sketches for a presentation at the 2007 Northern California NCTM math conference at Asilomar, California. They show very visually why the Law of Cosines is a variant of the Pythagorean Theorem. In fact, the Law of Cosines is a more 'generalized' version of the Pythagorean Theorem. Clicking on the *'Name'* of the file at the left will take you to the 'Instructor' version. Clicking on the *'Picture'* will take you to the 'Student' version.
69. Impossible Triangle ?	An "Impossible" Triangle ? Inspired by former student Gary McMurrin This impossible triangle rotates, stretches, and changes colors.
70. Can Sketchpad Think ??	Does The Geometer's Sketchpad have the ability to think, reason, and make decisions ? Scott Steketee has created some 'Boolean' Tools that do just that !!
71. DynaGraph Solutions	You can use DynaGraphs to solve equations !
72. Sketchpad'sModules	The Geometer's Sketchpad has many "modules" (book + CD) that are available from Key Curriculum Press They are displayed in this sketch in the form of a "*moduler* merry-go-round". Algebra One, Geometry, Algebra Two, Conic Sections, Pre-Calculus, Calculus, Pythagoras Plugged In, and Rethinking Proof.
73. ParametricColoring	Parametric Coloring in Sketchpad involves controlling the colors of an object using varying numerical values .
74. Marilyn Vos Savant	Marilyn Vos Savant was listed in the Guinness Book of World Records for five years under "Highest IQ" for both childhood and adult scores. Since 1986, Marilyn has been writing the "Ask Marilyn" question-and-answer column for Parade, the Sunday magazine. Marilyn is married to Robert Jarvik MD, the inventor of the Jarvik heart. Check out this "Sketchpad" version of one of her posted math problems.