Math - Understanding Geometry
Geometry is more than about measuring angles and circles or anything to do with shapes. Although that is a big part of this subject, there is a key to how they relate to real life use.
The key is logic. You might think that you only need this logic when building things, but you can use this skill of deductive reasoning in everyday life.
Geometry has a basic set of postulates and theories. You must have them memorized and understand those principles before you can move too far into this subject. Once you get a grip on them, you must be able to reason how you get from point A to point Z using those principles. This is where your skills of logic come in. It is not merely a matter to accept the final result, but to understand the process of coming from the beginning to the end.
Engineers and scientists will need Geometry in their professional fields. All students who plan to enter college need this skill to graduate. For them, it is mandatory to learn this subject.
For everyone else, the ability to think in a logical manner will save you from making a lot of wrong choices. Geometry will help you get there, even if though it is more than likely you will never use the formulae or equations you learn in class the rest of your life. The important thing you will take from this class is the ability to think and reason.
Here are some resources to help you get started:
Books
All the Math You'll Ever Need: A Self-Teaching Guide
Geometry and Trigonometry for Calculus: A Self Teaching Guide
Master Math: Pre-Calculus and Geometry
Geometry
- Geometry in Action - explore various areas in which ideas from discrete and computational geometry meet real world applications.Gallery of Interactive GeometryMrs. Glosser's Math Goodies - free educational web site featuring interactive math lessons with a problem-solving approach.Native American Geometry - a physical, proportional geometry that originates from the simple circle. Art and mathematics seemlessly integrated in Nature's geometry, emphasizing multiple intelligences and multi-cultural instruction.Geometry of the Sphere - provides basic information about spheres, looks at Girard's Theorem, and proves Euler's formula.
- Ben Sisko's Higher Dimensional Page - contains research on higher dimensions. There are five theories and theoretical applications.
- Categorical Geometry - contains online books and research papers on categorical geometry and categorical algebra.
- Erich's Packing Center - packing geometric shapes into other geometric shapes: circles in triangles, circles in circles, and much more, plus combinatorial geometry problems.
- Gallery of Interactive Geometry
- Gallery of Mathematical Surfaces
- Geometry - includes a special page on constructions and plenty of sample problems to help you understand the concepts.
- Geometry Center - resources and reference materials from this mathematics research and education center at the University of Minnesota.
- Geometry Formulas and Facts - excerpts from the 30th edition of CRC Standard Math Tables and Formulas covering geometry in two and three dimensions.
- Geometry in Action - explore various areas in which ideas from discrete and computational geometry meet real world applications.
- Geometry in Motion - interact with geometric diagrams via Java Sketchpad.
- Geometry of the Sphere - provides basic information about spheres, looks at Girard's Theorem, and proves Euler's formula.
- Isard - downloadable, interactive geometry software package written in Smalltalk.
- Leningrad Geometric School - a famous collective body of Russian geometers that rejected the methods of differential geometry.
- Logical Art and the Art of Logic - learn about pentominoes and what they have to do with Escher, Penrose, logic, impossible objects, mathematics, and art.
- Mathlab.com - Java applet providing virtual straightedge and compass for online interactive geometry.
- Mr. Field's Math Web Site - class projects in high school geometry and advanced algerbra.
- Mrs. Glosser's Math Goodies - free educational web site featuring interactive math lessons with a problem-solving approach.
- Native American Geometry - a physical, proportional geometry that originates from the simple circle. Art and mathematics seemlessly integrated in Nature's geometry, emphasizing multiple intelligences and multi-cultural instruction.
- Peek - a program to interactively visualize arbitrary n-dimension polytopes through the use of cross-sections and projections.
- Ptolemy's Ptools - where no kid has gone before in geometry. Use similar triangles to explore the world from your backyard and 3D worlds from your computer.
- Visual Dictionary of Special Plane Curves - including description, history, formulas, properties, and links for each.
- VRML Geometry Teacher - helps students visualize 3D objects.
- Wallpaper Groups - plane symmetry groups.
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