Additional Math Pages & Resources

Monday, November 8, 2010

American vs Italian Geometry

I saw a book called the Geometry of Pasta, and decided that it could entertain us today in the math blog. After all, geometry is clearly math. There were several very positive book reviews on Amazon, and one disgruntled review entitled "Another reason to hate geometry."

The reviewer goes on to say, "I was hoping for ... a book that would teach me about the various pastas and how to use them ... the graphic images are artsy, but useless. They are black and white ... look like art deco wallpaper or bed sheets".  

Here's a sample. What do  you think?

You can take a look at all of the pasta shapes here.

Being a writer and editor, I enjoy reading book reviews, and I think it's fair for a reader to be irritated by images of an item if they don't help connect what an item is (identity / name) to what it looks like (appearance / shape) and what you can do with it (utility / cooking).

If, like me, you grew up without Italian relatives or friends, you may not understand pasta from these pictures. I moved to the page with an alphabetical list of pasta and clicked on BUSIATI. It turns out to be a twisted worm-like shape marked 180 x 10 that's good with Pesto Genovese.  I think pesto is a green sauce and Genoa is an Italian town, but I've never had a basic pasta course, and these references baffle me.

(Yes, you are correct. I cannot successfully order pasta in an Italian restaurant.)

Remember last Friday's blog on DysLexia and DisCalculia?

Perhaps I have DisPastalia!

Let's cut through this confusion - here's what we at Excel Math consider geometry:

Identifying shapes by appearance and feel
Identifying straight and curved lines
Finding the inside and outside of a figure

Counting sides and corners
Navigating a maze

Learning terms: parallel, intersecting and perpendicular lines
Learning terms: of plane, figure, polygon, quadrilateral, parallelogram, and diagonal

Learning terms: flat and curved faces, vertices and edges
Learning terms: pentagon, hexagon, octagon and pentagon

Learning terms: rhombus and trapezoid

Recognizing 2-D figures: squares, circles, triangles and rectangles
Recognizing 2-D figures: equilateral, isosceles and scalene triangles
Recognizing 2-D figures: the parts of a circle
Recognizing 2-D figures: right, obtuse and acute angles

Recognizing lines of symmetry
Recognizing 3-D figures: sphere, cone, cylinder, cube, 
Recognizing 3-D figures: rectangular, square and triangular pyramids and prisms

Recognizing patterns
Recognizing when figures are similar or congruent

Recognizing movements: flips, turns and slides
Recognizing patterns in a sequence of figures or shading

Sorting shapes by common characteristics
Changing shapes by moving or removing lines
Drawing shapes from verbal descriptions
Creating shapes using pattern blocks
Finding simple shapes within complex patterns

Determining when figures do and do not belong in a set
Determining coordinate points
Determining if coordinate points are on a given line

Measuring line segments to the nearest half inch or half centimeter
Measuring angles
Measuring vertical or horizontal lines by subtracting X or Y coordinates

The sum of the angles for rectangles, triangles and circlesAssociating 360 degrees in a circle with 1/4, 1/2, 3/4 and full turns

Calculating area of a square and rectangle

Calculating perimeters
Calculating volume of a figure with one or more layers of cubes
Calculating the diameter, given the radius
Calculating the volume of a rectangular prism using the formula L x W x H
Calculating area and perimeter given coordinates on a coordinate grid

Calculating the area of a parallelogram
Calculating the surface area of a rectangular prism
Calculating the area of a triangle

Solving word problems involving area and perimeter

That's no doubt more than enough to make you groan or weep. I'll finish with this:  

Is the formula for the area of a pizza pie expressed as 2 π r, or is it π r²?

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