Document Sample

Math Art Computer Graphics Math Art Grades 7-12 Colette Stemple Coral Reef High School Miami, Florida Math Art Contents Page Teacher Statement 1. Course Overview Adobe ® Photoshop™ proves that Math is Beautiful Course description Course Goals 2. Summary of State Standards 3. Technology Specifications 4. Lesson Plan Table 5. Detailed Lesson Plans 6. Evaluation Form 7. Lesson Ideas 8. Bibliography 9. Tutorials and Gallery of Projects Math Art Computer Graphics Photoshop Mathematical Visualization Colette Stemple Coral Reef High School Miami, Florida TEACHER STATEMENT The connection between Photoshop and Math became apparent to me when I launched the first version of Photoshop in the middle school art program. Students began experimenting with actions, paths, and filters and began applying "visual math” to their imaging projects. Because they were working on Art projects and could see the concepts, and watch changes as they altered curves and percentages or worked with graphs, they were able to apply math concepts with ease without really knowing that Math was what they were doing. Even though these exercises were not formal math projects math scores improved for each of these students as a result of their visual experimentations. This course will introduce a series of Math Art exercises that have been formalized by International Baccalaureate students at Coral Reef High School. The messages of these exercises is that reinforcing lessons from any discipline by creating hands on visuals with the Art teacher Colette Stemple and approaching the process through play, imagination Reviewing Math Art Project Digital Compass and creative exploration, is a wonderful extension of any subject or discipline. Math Art ART AS THE HUB If teachers from other disciplines will let the art teacher aware of the mathematical principles inherent in the creation know what they are teaching, all concepts can be of visual images. With Adobe Photoshop, these principles reinforced through visual exercises. This has been are inherent in the process of creating art on the computer. demonstrated for centuries by actual man made objects as evidenced in cave paintings, arts and crafts and Adobe Systems software used across the curriculum in all of architecture throughout history. Now we also have the the classrooms and computer labs helps administrators, option of using the computer to help achieve these goals. teachers, parents, and the students to cooperatively get And, in the art classroom, the actual creation of an art work more out of, and put more into learning. Adobe software can often spontaneously spark the "genius "core in each offers a cohesive visual language and form of expression child that applies to every classroom situation. It "De-isolates", teachers and their subjects, it makes everyone's job easier In many schools, students move from one room, one and more fun. subject, and one teacher to another all day long, and never see connections from one subject to another. Most states have Math Rubrics and a Curriculum that teachers must follow. By working with the math teacher and applying these requirements to art exercises, the Art teacher can demolish the erroneous, long held, idea that Art is a frivolous elective and establish the art curriculum as the core of any discipline. The Art classroom is the place where all disciplines can and should all come together. As an Art teacher I have shown how this can happen by helping the Math teachers bring concepts to life and improving math comprehension by simply giving students some examples of how to be Math Art COURSE OVERVIEW The students were not obliged to get their creations "OK'd" by the Math Coarse Description: teacher, although that could certainly be a wonderful way for the Math These lessons and exercises are not meant to be Math Workbook teacher to connect to the creative core of the person they are trying to Lessons, though some could be used as such. Some of these teach. Exploring images made by students could indicate a "thinking" examples illustrate actual math concepts literally and accurately, pattern in a student's mind that the teacher could tap into and exploit. others are uninhibited play based in diverse mathematical themes or Also, art works could start lively discussion about Math principles in the focusing on the “MATH TOOLS” inherent in Photoshop. The lessons Math Room and not just in the Art Room. Math Art lessons should were created for use by Art Teachers, to allow them to use art to trigger the heart and imagination of each student and allow them to reinforce mathematical concepts, rules and explorations. This course share those qualities in the Math classroom. If the Math teacher doesn't module was designed for artistic explorations in the realm of have the skills to create these opportunities for visual learning, then the mathematical structures, laws, deviations and explorations. Art should be called upon to help. The course module I created is a nine week project for students from all academies, on each level of mathematical and artistic expertise. The only instructions they needed was to remind them of the incredibly diverse amount of information they have learned in Math classes and also Science classes and then challenge them take one or more principles or theories and create a simple work of visual art that reflects these principles and theories. This made it possible for students to take one discipline, Art and another discipline, Math, and put them together to see that they were inseparable. Of course, this leads too a great deal of lively discussion and collaboration among the students which also sparks learning. No emphasis was placed aesthetics. In some exercises it is easy to that this was not stressed. However, some students started to see it themselves as artists as their "Math ideas" became pictures and this sparked the wonderful result of making them want to keep working on to achieve an aesthetic that they considered acceptable. Course Goals: This workbook is intended to encourage all teachers to share their Digital Compass Project comprehensive tests, standards and lessons with the art teacher. Though it is not the Art teacher's job to teach Math, Science, Language Arts or Computer Literacy but that is exactly what happens when art class is combined with any other discipline. Math Art State Standards Florida State Standards Technology Specifications Florida Department of Education Sunshine State Computer Specifications: Standards-Visual Arts 9-12 20 PC computers, Pentium III Processors, 128.0 MB RAM 2 HP Deskjet 870 CXI color Printers Skills and Techniques: 1 HP Deskjet 1600 CM Color Printer Standard 1: The student understands and applies media, 2 HP Scanjet 6100 C Flatbed Scanner techniques and processes. VA.A.1.4 2 Epson Stylus Photo 1270 Inkjet printers 1 Fuji FUJIX 3000 Dye Sublimation Printer 2 Canon CanoScan FS 2710 negative & transparency scanners Cultural and Historical Connections 20 12” Wacom Tablets Standard 1: The student understands the visual arts in relation to history and culture. VA.C.1.4 Adobe Software List: Aesthetic and Critical Analysis Adobe Photoshop 7.0 Standard 1: The student assesses, evaluates, and Adobe® GoLive ™ responds to the characteristics of works of art. VA.D.1.4 Adobe® Illustrator ™ Applications to Life Adobe® Atmosphere ™ Adobe® Acrobat™ Standard 1 The student makes connections between the visual arts, other disciplines and the real world. VA.E.1.4 For more information about the Florida Sunshine State Competency Based Standards go to: www.firn.edu/doe/menu/sss.htm Math Art Lesson Plan Table 1. Review Math Concepts and Visualization See Bibliography** Start with the BLACK HOLE Review Photoshop Tools Photoshop & Photoshop by O’Connor Elements Tutorials* Photoshop or Elements* 2 Simple Algebraic Graphing Graphing Equations from any See DIGITAL COMPASS Creating a simple x axis and y axis graph and elaborate Algebra book. Exercise by Marraccini 3. Review Perspective (as in the Renaissance), Foreshortening and Atmospheric 1, 2, & 3 point perspective 3D transform tool 9th Perspective (as in Photo Realism) samples Grade samples using & from Art texts Sample PHOTOGRAPHS by Curtis Chan 4. 2D Design as defined in Abstract Art Art History texts & URLs G. Yap & C. Chan samples. 5. Saturation and the Properties of Color and Light (as in Impressionism), Value Color Theory, Intensitiy, Christina Jay and 9th grade Scale Saturation, Scales Sample Color 6. Pattern and Symmetry (as in Islamic Art) Art History texts & URL's N. Salz Formal Symmetry samples 7. Digitization (as in Photo Imitation), Computer Graphics, The Art of Chuck Close & Enlargements of any Computer Engineering and Photo Realism Rasterization, Pixels etc. Rasterized Image Computer Engineering Photos by J. Jing Zeng 8. Geometric Abstracts using all types of Angles The Art of Richard “Propriano”, Mortensen’s Basic laws of motion in physics Mortensen. S. Delauney, M. abstract painting; study of the Weber measurement of angles. Sample & Natural Elements by G. Obermeier (9 gr.) Math Art Detailed Lesson Plans THE VISUAL ARTS LESSON PLAN Show Art and Mathematical examples of both. LEVEL 1 Discuss OP ART, Convergence, Performance Assessment: Vortex, Perspective, Emphasis, Depth of Field, Observation: All Lessons illustrated in this workbook Concentricity, Space, Unity, were developed by the students in Illusory Motion, & Space Final Project: Visual Arts Level I. Group Critique of individualized re- interpretation of the Vocabulary: Assignment Each student was evaluated and All of the words in Procedures with emphasis Observation of student working graded according to the components on the correlation of Mathematics with the Self - assessment by the student shown below for this course. Elements of Visual Composition Journal Entries Sketches Materials: Photoshop or Photoshop Elements Sketchbook/ Journal or Homework: Base Assessment: Do sketches in the Journal of the Vocabulary test Media: concepts introduced. Design creation Computer Imaging List possible Design Applications List possible Mathematical Applications Visual Resources: Photoshop or Elements tool tutorial if necessary. See Evaluation Form following page. Show examples from the imagination, nature and existing Art and Mathematical forms or functions. Procedures: Show students how to open Photoshop and Show how a simple concept can lead to instruct with handout a basic diagram of the advanced theories in Physics, Calculus, tools. Geometry, and Algebra Give a background with Art History examples Show where Symmetry both Radial and of Formal and Radial Symmetry and discuss Formal have dominated centuries of Design in the concept of Compositional Centering different cultures and religious iconography. Math Art Florida Sunshine State Standards for Teacher and Student Evaluations. Course Name___________________________________________________________________________________ Student Name__________________________________________________________________________________ Student State Standards-Performance Assessment Teacher Grade Evaluation evaluation I. Skills and Techniques: Standard 1: The student understands and applies media, techniques and processes. VA.A.1.4 II. Cultural and Historical Connections Standard 1: The student understands the visual arts in relation to history and culture. VA.C.1.4 III. Aesthetic and Critical Analysis Standard 1: The student assesses, evaluates, and responds to the characteristics of works of art. VA.D.1.4 IV. Applications to Life Standard 1 The student makes connections between the visual arts, other disciplines and the real world. VA.E.1.4 V. Observation: Math Art MATH LESSON IDEAS 1. Analytic Geometry, Bi Lateral Symmetry, Rotational Symmetry, Curves 2. Graphs: Equations and Slopes of Lines, Tessellations or Tiling, Perspective, Histograms, Scale, Pattern _ Rhythm, Sierpinski Triangles, Fractals, 3. Tangents, 2D & 3D Geometric Shapes, Saturation, Spherical Coordinates, 4. Parametric Equations, Tangents, Drag: (e.g. Marine objects with least drag are torpedo shaped and are ¼ wide as they are long.) 5. Area & Perimeter, Diameter and Radii, Segments, Transformations, Rotations, Reflections, Positive vs. Negative, Bezier Curves, Mandalas, 6. Contours, Values, Shades, Series, Syncopation, Perimeter, Area, Volume Graphing, Histograms. LESSONS WITH FOUNDATIONS IN ART AND CULTURES 1. Perspective (as in the Renaissance) 2. Value Scale 3. 2D & 3D Design, (as in Abstract Art) 4. Saturation, and the Properties of Color and Light, (as in Impressionism) 5. Pattern and Symmetry (as in Islamic Art) 6. Foreshortening and Atmospheric Perspective (as in Photo Realism) 7. Digitization (as in Photo Imitation) 8. Geometric Abstracts (as in Rayonism) 9. Mathematical Languages ( as in Abstraction, Symbolism, Architectural Construction, Cubism) 10. Proportion and Distortion and Illusion (as in Surrealism). 11. The SUMBA CULTURE of Indonesia 12. WESTERN APACHE CRAFTS and all Native American & African Crafts Math Art 13. HELLENISTIC POTTERY of Greece 14. LANDSCAPE & STILL LIFE PAINTING from any period & place 15. MASTERS OF LIGHT DEFINITION from the Renaissance to the Present 16. CUBISM Its masters, prototypes, and imitators 17. OP ART 18. TROMPE L’OEIL especially in French & Dutch Art of the Renaissance 19. RAKED GARDENS OF JAPAN 20. ARCHITECTURE from any time and place 21. FUTURISM, DE STIJL, CONSTRUCTIVISM, SURREALISM, SUPREMATISM 22. NEOCLASSICISM especially Jacques Louis David & Jean Auguste Ingres 23. POST IMPRESSIONISM especially Paul Cezanne 24. EXPRESSIONISM especially Henri Matisse & Wassily Kandinsky Math Art BIBLIOGRAPHY 1. Art & Physics Parallel Visions in Space, Time & Light, by Leonard Shlain, Quill William Morrow New York, 1991 2. Exploring The Invisible (Art, Science And The Spiritual,) by Lynn Gamwell, Princeton University Press, 2002 3. Schoolworks Photoshop Elements , for Teachers, by Barbara and Nickolas Delikaris, Schoolworks, 2003 4. Discovering Geometry, An Inductive Approach, by Michael Serra, Key Curriculum Press 5. The Genesis of Form, From Chaos to Geometry, by Mark Verstockt, Muller, Blond & White 6. Symmetry in Chaos, A Search for Pattern in Mathematics, Art, & Nature, by Michael Field & Martin Golubitsky, Oxford Press 7. Visualization, The Second Computer Revolution, by Richard Mark Friedhoff and William Benzon, W.H. Freeman & Co. 8. Cellular Automata and Complexity, Collected Papers, by Stephen Wolfram, Westview Press, 1994 9. Algebra to Go, A Mathematics Handbook, by Great Source Education Group, Houghton Mifflin Co., 2000 10. Key to Geometry Skillbook Series # KJ100, by Lakeshore Basics ON-LINE RESOURCES www.didkblick.com/zz720/64 Integrating Technology in Science & Math Instruction www.bennett.edu/academic/nfs Yahooligans! Arts & Entertainment: Art www.yahooligans.com/Arts_and_Entertainment/Art Welcome to Integer Jim’s Math Squad www.mathsquad.com Index Vance & Art’s Spell Bound Game and Math Puzzles and Games http://web.pdx.edu/~manchest/ ADOBE EDUCATION SITE, wwwladobe.com/education Math Art Mathematics – k – 12 Internet Sites http://archives.math.utk.edu/k12.html PiRanch Math Camps, Unique Art, Algebra Camp, Geometry Camp etc. www.piranch.com/schedule.htm dvdream.com art instruction catalog www.dvdream.com/dover_art_instruction_catalog.html Kathy Schrock’s Guide for Educators – Mathematics Resources school.discovery.com/schrockguide/math.html Art Links www.rcs.k12.va.us/csjh/artlinks.htm 2002 AMTNJ Symposium: Using Computers to Enhance Math Instruction mathforum.com/~shelly/presentations/AMTNJ/10.2002.html Art Instruction Books www.rhodemap.com/store/books/artinstruction.htm Cool Math Sites www.cte.jhu.edu/theacademy/web/2000/heal/mathsites.htm Fun Math www.surprise.com/kids/math_skills/fun_math_program.cfm Deliberately Distorting The Digital Mechanism Site www.jodi.org,asdfg.jodi.org; 404.jodi.org, wrongbrowser.com & www.jodi.org, mirapaul@nytimes.com Math Art TUTORIALS Adobe Photoshop 7.0 M. O'Connor Template Project TEMPLATE TUTORIAL Copy Layer Photoshop 7.0 Rotate New Layer 90 degrees 1. Pull down the File menu and select new. Copy Layer In the dialogue box set Rotate New Layer 90 degrees 50 Pixels/inch 5 in x 5 in 2. In the toolbox select the Geometric Lasso Tool Create a spiral in towards the center, and then follow it back out. 3. Double click the foreground color box in the Color Picker at the bottom of the toolbox and select the color Red as the foreground color 4. Pull down the Edit menu and select Fill In the dialogue box select foreground color The will fill selection with red. 5. Pull down the Filter menu and select Distort>Twirl In the dialogue box set the Amount to –150 to –100 or 100 to 150 depending on the direction of the twirl you want to create Select OK and the lines on the image will twirl into a spiral 6. In the Layer menu select New Layer A new layer will appear in the Layer window 7. In the Layer menu select Layer Properties In the dialogue box Add drop Shadow seta t 120 degrees TEMPLATE Copy Layer M. O’Connor Rotate New Layer 90 degrees Math Art BLACK HOLE TUTORIAL BLACK HOLE Photoshop 7.0 File Menu: M. O’Connor New Image 150 pixels/inch 5 inches x 5 inches Edit Menu: Fill Fill Layer with Black Image Menu: Mode Screen Filter Menu: Add Noise… Gaussian Monochrome Image menu: Adjustments: Adjust levels Drag Far Left (Black) Arrow Right. Filter Menu: Blur> Radial Blur Amount: 25 Math Art Tessellation Tutorial Layer Menu: Photoshop 7.0 Copy Layer. Fill Selection with black. File: New Image Edit Menu: 150 Pixels/inch Fill, Fill background with white. 5 in x 5 in Layer menu: Edit: Align black and red selections. Merge Layers. Fill >Background with black Edit Menu: Toolbox: Copy Layer with black and red. Paste Rectangular Marquee Continue copying until image is full. In foreground, create a square that Is approximately 1/16th of the screen size Fill Background with black Edit: TESSELATION Fill>Fill Square with color (red) M. O’Connor Toolbox: Lasso tool: Create a selection including only parts from the right size of the square. Rectangular Marquee: Select half of square Edit Menu: Copy Selection Paste selection on a new layer Move selection until it is flush with opposing side. Layer Menu: Merge New layer with square layer Repeat process for top and bottom. Do not cross outside of the square when making selection. Math Art Cage and Curl Tutorial 7. In the toolbox select the Rectangular Selection Tool Photoshop 7.0 Make Vertical selections that extend from the top to the bottom of the image area 1. Pull down File Menu and create a New Image file In the dialogue box, use the following parameters 8. Pull down the Edit Menu and select Fill: 150 pixels/inch Fill each selection with 100% Black. 5 inches x 5 inches Each rectangle should look like a line Repeat Process with Horizontal Lines 2. Select the Paint Brush from the Toolbox and the Airbrush tool from the These lines will form boxes that indicate a cage menu bar Choose Color: Black The boxes should look tilted because of the swirl behind them. Set the brush size to Size: 35 (Soft) CAGE CURL 3. On the blank image Create Lines Create several Vertical Lines and Several Horizontal Lines. M. O’Connor Do not make them completely straight. 4. Pull down the Filter menu and select Distort>Pinch Set the Pinch to 100% 5. Pull down the Filter menu and select Distort>Twirl Set the Twirl to 72% Select OK and the original pinched lines will twirl 6. In the Layer menu Create a New Layer. Be sure this layer is selected in the Layer Window Math Art TUTORIAL PHOTOSHOP 7.0 UNRAVELLING UNRAVELLING M. O’Connor File Menu: New>New Image 150 Pixels/inch 5 Inches x 5 inches Toolbox: Paintbrush tool Color: Black Size: 35 (Soft) Create Lines Create several Vertical Lines and Several Horizontal Lines. Do not make them completely straight. Filter Menu: Polar Coordinates:>Rectangular to Polar Math Art TUTORIALS PHOTOSHOP 7.0 MATHEMATICAL DISTORTION R. Fackler Science Major In this exercise, I took a photo of my brother, added mathematical principles of geometry and algebraic graphing and turned the picture into a work of art. I believe you can make any subject fun by applying basic math principles to photographic images. This project allowed me to use my creativity while using the math concepts I have learned over the last four years. Rendered Brother- applied to a photograph based on the geometric principles Head embellished by using a sphere shape on a 35-degree angle field of view: 1. Pull Down the filter menu> Render>3-D transform. 2. Choose the sphere shape from the toolbox 3. Draw around the head 4. Tilt the sphere at a 35 –degree angle. This made the head almost look 3-D while the rest of the picture was flat. I thought about using other shapes to accent his body shapes, however it drew away from the essence of the geometric figures. POLAR COORDINATES R. Fackler Math Art MATHEMATICAL DISTORTION R. Fackler Polar Coordinate Brother- Modifications to a photographic image using mathematical concepts of algebraic graphing. Distortion One: 1. Start with the equation x = y 2. Set the image on a vertical slope at the points (0.0) on the x/y axis. This pulled the picture into the center of the graph distorting the picture into an oval shape. Distortion Two: 1. Select the Filter Menu>Distort> polar coordinate. 2. Choose the option rectangular to polar. Mathematical Distortion R. Fackler Math Art Math Concepts Polar Coordinates-Graphs: Illustrating Geometric Shapes: R. Fackler Centering equidistant to the midpoint: Filter/Render/3D Images Science Major Pulled image area into 0-0 on x-y axis Selected Cube Created an Oval of the original shape Tilted Axis by 15 degrees Math Art DIGITAL COMPASS P. Marriccinni Step 1. Open a new file that is 1200 by 1600 pixels and make a graph that ranges from at least 6 to –6 on the x and y axis using the line tool. Make a mark the x-axis and y-axis every 100 pixels. Make sure you use the rulers to make sure the space between each number is exact. Step 2. Draw the line y=x using the line tool. Start at point (-5, -5) which is 1300 pixels on the vertical line and at 100 pixels on the horizontal ruler. Then draw the line to point (5,5) which is 300 pixels on vertical ruler and 1100 pixels on the horizontal ruler. Draw the line y=-x, which starts at (- 5,5) which, is 300 pixels on vertical and 100 pixels on the horizontal ruler. Then end at point (5, -5) which is 1300 pixels on the vertical and 100 pixels on the horizontal ruler.. Math Art Step 3. Draw the line y=0 and the line x=0. They are on your axis but only draw them from 6 to –6. Math Art Step 4. Select the pen tool and make 3 anchor points on the line y=-x. One at where it started, one on the origin (0,0) which is 800 pixels on the vertical and 600 pixels on the horizontal ruler. Math Art Step 5. Hold down shift and click on the anchor point at the origin. Then move the mouse to make a curve. Then let go of the shift key and the mouse. Math Art (Step 5. Hold down shift and click on the anchor point at the origin. Then move the mouse to make a curve. Then let go of the shift key and the mouse.) Step 6. Repeat Steps 5 except make the curve the opposite way Math Art Step 7. Repeat step 6 for new curve (Step 6 Go to the anchor point on the end of the line that does not have the curve hold down shift and click on it. It will automatically make the curve for you.) Math Art Step 8. Repeat for line y=x Math Art Step 9. Repeat for line y=0 Math Art Tutorials Step 10. Finish line y=0 Math Art Tutorials Step 11. Make curves on line x=0 Math Art Step 12. Make a new layer with 30% opacity. Then write in the equations for some of the lines used next to them to label them. Math Art Step 13. Make new layer 100% opacity and label the units on the graph. Math Art Final Step. (Optional) Color in graph and add filter. Math Art STEP BY STEP THROUGH THE HISTORY PALLETTE History: - paint bucket - ellipse - ellipse - ellipse - ellipse - pattern fill 1 - liquefy - liquefy - line - line - line - line - line - line - line - line - pattern fill 1 - lens flare Math Art History: - pen - pen - pattern fill - ellipse - ellipse - pattern fill - ellipse - pattern fill - liquefy - liquefy - 3D transform Math Art Math Art TUTORIALS Adobe Photoshop 7.0 The figure above was drawn with the polygonal and the elliptical selection tools. The Foreground and Background colors were set to Black and White and the Gradient Tool was used to fill in the shapes. The letters were created by hand using the Pencil Tool, working with black in the white areas and white in the black areas for visibility. The figure above illustrates a surprising fact about triangles and circles. Given any triangle, within the A, B, C, points there is a circle that contains all of the following nine points: 1. The midpoints K, L, and M of the sides of the triangle ABC. 2. The points X, Y, and Z, where AX, BY, and CZ are the altitudes of triangle A, B, C. 3. The points R, S, and T, which are the midpoints of the segments AH, BH, and CH that join the vertices of triangle ABC to the point H where the lines containing the altitudes intersect. Math Art GALLERY OF STUDENT PROJECTS J. Williams To create this image I used the ellipse tool, the rectangle tool, the custom shape tool, the rounded rectangle tool and the polygon tool. I duplicated the shapes and used the Emboss Filter tool in the Stylize section of the Filters menu. Math Art This image was inspired by the lesson in geometric relationships on the classifications of quadrilaterals. It was created with the polygonal lasso, the gradient tool, the rectangular selection tool and the paint brush tool. Math Art This painting was done with the Adobe Photoshop. Tools used were the Paintbrush, Pencil, Polygonal lasso tool, Paint Bucket and Color Selection Tools. The Lasso was used to draw the shapes and the Paint Bucket and Brush Tools were used to fill in the colors. The paint Brush and the Pencil were used to draw in the lines and details. This lesson was designed to teach Mathematical Concepts using Art History for inspiration, in this case Richard Mortensen’s work, and Adobe Photoshop for execution. Math Art To make the picture above: 1. Create a background with the gradient tool 2. Use the Filter Menu to create and color shapes: - Create shapes with the 3D Transform filter and the Cutout filter - Create effects with the Glass filter and the Lighting Effects filters. Math Art Math Art Math Art Math Art Shapes One Shapes Two Math Art Math Art Math Art STELLAR NAVIGATION G. Yap

DOCUMENT INFO

Shared By:

Tags:

Stats:

views: | 344 |

posted: | 2/8/2010 |

language: | English |

pages: | 49 |

Description:
Department of Mathematics, math games, the Math, applied mathematics, Graduate Students, math skills, math help, math textbook, math homework help, flash cards, Symbols, Symbol,math

OTHER DOCS BY deathlove

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.