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N-Space:

N-Space:. or. Mathematical Object?. Boy Band. Erik Scott Highline Community College. “Doing math 22/7?!! Are you nuts?”. Math as Puzzles (CMRL Math).

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N-Space:

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  1. N-Space: or Mathematical Object? Boy Band Erik Scott Highline Community College

  2. “Doing math 22/7?!!Are you nuts?”

  3. Math as Puzzles (CMRL Math) Try to connect the two dots below using a combination of red and blue arrows. Each red arrow means “add six” and each blue arrow means “subtract fifteen.” Can it be done? 11 4

  4. Geometry and the Structure of the Universe • Geometry in Chemistry: Geometry in Physics:

  5. The Magical Symbols of Mathematics • In Algebra: In Calculus: In the Sciences:

  6. They can even be used as a signature:

  7. Comparing dimensions visually: • A two-dimensional (2-D) image: A “three-dimensional” (3-D) image:

  8. What is a dimension? • It is a category we use to describe something. For objects: “Height” or “Width” For people: “Honest” or “Fun”

  9. How does a person decide if something is 1-dimensional, 2-dimensional, etc? • Think of the different adjectives you could use to completely describe the quantity, object, or person. • Group the adjectives into categories. • Eliminate redundant categories to find the smallest number of categories required. • Count the number of categories to obtain the overall dimension of the object.

  10. Descriptions of the categories we’ve found: • Category 1: My placement left to right. • Category 2: My placement front to back. • Category 3: My placement up and down. Notice that all three descriptions are completely distinct – adjectives from categories 1 and 2 are not enough to describe category 3.

  11. Mathematical Equivalents Spanning Set– This is our requirement that the collection of categories completely describe the situation of interest. • (Linear) Independence – • This is our requirement that each category is not describable by a combination of descriptions from other categories. Basis – A set of categories with the two properties listed above. It’s the smallest, most economical collection of categories.

  12. Cloud Nine,orJust a Nine-Dimensional Subspace?

  13. Personals Ads:

  14. The span of one vector:Marital Status S M D

  15. The span of two vectors:Marital Status and Race/Ethnicity SA SB SW SH MA MB MW MH DA DB DW DH

  16. The span of three vectors:Marital Status, Race/Ethnicity, and Gender SHM MHM DHM DHF SWM DWF SBM DBF SAM SAF MAF DAF

  17. The space searched by Match.com may be 14-Dimensional!!

  18. Spaces of Interest to Mathematicians This is a set of functions with basis 1, x, x2, x3, …. that includes functions such as • Infinite-dimensional spaces:

  19. The Klein Bottle • and its familiar immersion into R3:

  20. The Klein Bottle in 4-D:

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