![Visualization
There are many different meanings of the word visualization. Outside
the domain of computer graphics, accepted definitions include
making visible, especially to one’s mind (thing not visible to the eye),
forming a mental image of something (thing not present to the sight, an
abstraction, etc.) [Webster70].
PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 3 / 20](https://image.slidesharecdn.com/krochin2017semfin-170315182740/85/Visual-Metaphor-of-Mathematical-Abstractions-and-their-Visualization-through-Newly-Uprised-PDF-document-Facielities-4-320.jpg)
Visual Metaphor of Mathematical Abstractions and their Visualization through Newly Uprised PDF-document Facielities
- 1. Visual Metaphor of Mathematical Abstractions and their Visualization through Newly Uprised PDF-document Facielities PhD Alexander L. Krochin Ural Federal University, Yekaterinburg, Russia 15.03.2017 PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 1 / 20
- 2. "Tell me and I forget. Show me and I remember. Involve me and I understand." — Chinese proverb Key words for open education: visualization + dynamic + interactivity PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 2 / 20
- 3. "Tell me and I forget. Show me and I remember. Involve me and I understand." — Chinese proverb Key words for open education: visualization + dynamic + interactivity PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 2 / 20
- 4. Visualization There are many different meanings of the word visualization. Outside the domain of computer graphics, accepted definitions include making visible, especially to one’s mind (thing not visible to the eye), forming a mental image of something (thing not present to the sight, an abstraction, etc.) [Webster70]. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 3 / 20
- 5. Visualization and modern teaching The visualization has been used in many areas of knowledge: architec- ture, medicine, science, software, information visualization, “big data” visualization, and so on. Here, the visualization of mathematical abstract entities and concepts is used to facilitate teaching/learning process and communication between teacher and students. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 4 / 20
- 6. PDF document standard Portable Document Format (PDF) (developed, improved and maintained by Adobe) is one of the wide-spreading document standards for platform- independent exchange. The main features of the file formats in the use of learning are: presence of the built-in JavaScript programming language; controlled multi-layered structure of the slide, which supports anima- tion and quasi-animation; possibility of introducing (embedding) multimedia objects; a built-in mechanism for interactive viewing of 3-dimensional objects from the embedded U3D and PRC formats source. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 5 / 20
- 7. PDF document standard Portable Document Format (PDF) (developed, improved and maintained by Adobe) is one of the wide-spreading document standards for platform- independent exchange. The main features of the file formats in the use of learning are: presence of the built-in JavaScript programming language; controlled multi-layered structure of the slide, which supports anima- tion and quasi-animation; possibility of introducing (embedding) multimedia objects; a built-in mechanism for interactive viewing of 3-dimensional objects from the embedded U3D and PRC formats source. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 5 / 20
- 8. PDF document standard Portable Document Format (PDF) (developed, improved and maintained by Adobe) is one of the wide-spreading document standards for platform- independent exchange. The main features of the file formats in the use of learning are: presence of the built-in JavaScript programming language; controlled multi-layered structure of the slide, which supports anima- tion and quasi-animation; possibility of introducing (embedding) multimedia objects; a built-in mechanism for interactive viewing of 3-dimensional objects from the embedded U3D and PRC formats source. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 5 / 20
- 9. PDF document standard Portable Document Format (PDF) (developed, improved and maintained by Adobe) is one of the wide-spreading document standards for platform- independent exchange. The main features of the file formats in the use of learning are: presence of the built-in JavaScript programming language; controlled multi-layered structure of the slide, which supports anima- tion and quasi-animation; possibility of introducing (embedding) multimedia objects; a built-in mechanism for interactive viewing of 3-dimensional objects from the embedded U3D and PRC formats source. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 5 / 20
- 10. PDF features in action PDF format documents with new interactive and dynamic facilities essen- tially improve the effectiveness of teaching/ learning process, especially in mathematics education. The main problem in preparation of PDF documents is developing an adequate visual metaphor and a suitable and inexpensive program in- strument for metaphor implementation. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 6 / 20
- 11. LATEX tool The LATEX (pfdLATEX) is the most popular text processor in academic society, that produces an exellent mathematical papers. Graphs and pictures can be produced by many graphical programs (Meta- Post, TikZ, Asymptote, etc.) and systems like the Maple with various output formats. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 7 / 20
- 12. Didactical capabilities Modern graphical tools allow one display dynamical images. One can control the level of inputs and outputs for logical transformations, formulae exploration; cover and recover the text and image fragments; possibility of introducing (embedding) multimedia objects; onscreen modelling (Buffon pin); PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 8 / 20
- 13. Didactical capabilities Modern graphical tools allow one display dynamical images. One can control the level of inputs and outputs for logical transformations, formulae exploration; cover and recover the text and image fragments; possibility of introducing (embedding) multimedia objects; onscreen modelling (Buffon pin); PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 8 / 20
- 14. Didactical capabilities Modern graphical tools allow one display dynamical images. One can control the level of inputs and outputs for logical transformations, formulae exploration; cover and recover the text and image fragments; possibility of introducing (embedding) multimedia objects; onscreen modelling (Buffon pin); PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 8 / 20
- 15. Didactical capabilities Modern graphical tools allow one display dynamical images. One can control the level of inputs and outputs for logical transformations, formulae exploration; cover and recover the text and image fragments; possibility of introducing (embedding) multimedia objects; onscreen modelling (Buffon pin); PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 8 / 20
- 16. Didactical capabilities Modern graphical tools allow one display dynamical images. One can control the level of inputs and outputs for logical transformations, formulae exploration; cover and recover the text and image fragments; possibility of introducing (embedding) multimedia objects; onscreen modelling (Buffon pin); The instructor want to explain to students how to solve some difficult proplem. Every steps of his explanation connect with certain picture associated with a particular image via appearing arrows. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 8 / 20
- 17. Dynamical explanation PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 9 / 20
- 18. Nice and effective tool is animation — a consecutive display of the pictorial sequence (animate.sty). The more faster animation can illustrate the Law of Large Numbers graphically. Convolution of a probability density functions of uniform distribution. Number of terms grows: two, three, four, to ten. As a result one can see: a triangle, and other curves, shown PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 10 / 20
- 19. Frames of didactical animation PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 11 / 20
- 20. Instrumental program tools for PDF format Graphical parts of documents are prepared by means of numerous free tools, occasionally, commercial programs. Popular assembly software based on LATEX contains almost all free graphic- aimed tools (MetaPost, TikZ, and Ps-tricks). So, the LATEX source scripts “collecting” text, graphics, and multimedia components and transform all in whole standard PDF document. The choice of specific programs for creating graphical objects is deter- mined by the specific features of visualization of mathematical mental images. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 12 / 20
- 21. 3D — images Let us distinguish an ordinary static drawing of 3D object named as quasi 3D and real or dynamical 3D images. Somebody can rotate letter, vary size, and change angle and direction of vision. Beside that, real 3D picture is much more informative and expressive, and that is important for educational purposes. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 13 / 20
- 22. There is free tool for demonstrate PDF documents in their entirety — Adobe Reader. But a convenient and suitable tool for making teaching materials is absent. Adobe Reader screen shots 3D model with drop-down control menu. PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 14 / 20
- 23. Sources for 3D images The 3D file convertion Maple and Mathematica — many output formats (real 3D): X3D, Collada(dae) . Useful for PDF — U3D, PRC — not available. .dae (Collada) ⇒ (via something — Blender) U3D ⇒ PDF (via movie15) .x3d ⇒ (maplex3d2prc) PRC ⇒ PDF (media9). PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 15 / 20
- 24. Sources for 3D images The 3D file convertion Maple and Mathematica — many output formats (real 3D): X3D, Collada(dae) . Useful for PDF — U3D, PRC — not available. .dae (Collada) ⇒ (via something — Blender) U3D ⇒ PDF (via movie15) .x3d ⇒ (maplex3d2prc) PRC ⇒ PDF (media9). PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 15 / 20
- 25. Sources for 3D images The 3D file convertion Maple and Mathematica — many output formats (real 3D): X3D, Collada(dae) . Useful for PDF — U3D, PRC — not available. .dae (Collada) ⇒ (via something — Blender) U3D ⇒ PDF (via movie15) .x3d ⇒ (maplex3d2prc) PRC ⇒ PDF (media9). PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 15 / 20
- 26. Sources for 3D images The 3D file convertion Maple and Mathematica — many output formats (real 3D): X3D, Collada(dae) . Useful for PDF — U3D, PRC — not available. .dae (Collada) ⇒ (via something — Blender) U3D ⇒ PDF (via movie15) .x3d ⇒ (maplex3d2prc) PRC ⇒ PDF (media9). PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 15 / 20
- 27. Sources for 3D images The 3D file convertion Maple and Mathematica — many output formats (real 3D): X3D, Collada(dae) . Useful for PDF — U3D, PRC — not available. .dae (Collada) ⇒ (via something — Blender) U3D ⇒ PDF (via movie15) .x3d ⇒ (maplex3d2prc) PRC ⇒ PDF (media9). Asymptote — embedding into LATEX(via pdfLATEX) or PRC and ⇒ PDF (media9) PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 15 / 20
- 28. Simple examples (dice3D) PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 16 / 20
- 29. (dissabbiatoremeshlab.u3d) Click here!PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 17 / 20
- 30. (plot3a.prc) Click here!PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 18 / 20
- 31. Example TUGboat, Volume 30 (2009), No. 1 s T - d e s e o Figure 1: An interactive 3D PDF of a B´ezier surface representation of the Utah Teapot.PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 19 / 20
- 32. Usage of 3D PDF Big massives of 3D data — the result of mesurement and calculation in many sciencies. And all these results may be embedded into PDF documents for easier perception, analysis, and discussion. Next slide is the complex moleculae image, calculatede from data. 15th March 2017 1 / 1
- 33. (plot3a.prc) Click here! 15th March 2017 2 / 1
- 34. Thank you for your attention! PhD Alexander L. Krochin (Ural Federal University, Yekaterinburg, Russia)Visual Metaphor of Mathematical Abstractions 15.03.2017 20 / 20