Tag: symmetry

Posted in GeoGebra worksheets, Geometry

The house of quadrilaterals

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In Investigating an Ordering of Quadrilaterals published in ZDM, Gunter Graumann shared a good activity for developing students mathematical thinking. The activity is about ordering quadrilaterals based on its characteristics. He gave the following list of different aspects of quadrilaterals as possible basis for investigation.

  1. Sides with equal length (two neighbouring or two opposite or three or four sides)
  2. Sum of the length of two sides are equal (two neighbouring or two opposite sides)
  3. Parallel sides (one pair of opposite or two pairs of opposite sides)
  4. Angles with equal measure (one pair or two pairs of neighbouring or opposite angles, three angles or four angles)
  5. Special angle measures (90° – perhaps 60° and 120° with one, two, three or four angles)
  6. Special sum of angle measures (two neighbouring or opposite angles lead to 180°)
  7. Diagonals with equal length
  8. Orthogonal diagonals (diagonals at right angles)
  9. One diagonal bisects the other one or each diagonal bisects the other one,
  10. Symmetry (one, two or four axis’ of symmetry where an axis connects two vertices or two side-midpoints, one or three rotation symmetry, one or two axis’ of sloping symmetry). With a sloping-symmetry there exists a reflection – notabsolutely necessary orthogonal to the axis – which maps the quadrilateral onto itself. For such a sloping reflection the connection of one point and its picture is bisected by the axis and all connections lines point-picture are parallel to each other.

The house of quadrilaterals based on analysis of the different characteristics of its diagonals is shown below. Knowledge of these comes in handy in problem solving.

House of quadrilaterals based on diagonals

Read my post Problem Solving with Quadrilaterals. You will like it.:-)

Posted in Math blogs

Math and Multimedia Blog Carnival #17

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WELCOME  to the 17th edition of Math and Multimedia Blog Carnival!

As is the tradition, a math blog carnival should introduce the mathematical significance of n in its nth edition. I was lucky to host this 17th edition. I didn’t have to look further for the significance of the number 17. The 17 beautiful patterns of wall paper groups is enough introduction for your eyes.

A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups. – from Wikipedia.

Now, on to the 17 math posts from your favorite math blogs and bloggers.

1. Guillermo P. Bautista Jr. who started the Math and Multimedia Carnival presents The man who conned a mathematician at Mathematics and Multimedia.

2, John Cook presents Poor Mercator posted at The Endeavour, saying, “Mathematics behind the Mercator projection”.

3. Romeo Vitelli presents The Boltzmann Mystery (Part 1) posted at Providentia, saying, “A two-part post on the strange life and death of mathematician and physicist, Ludwig Boltzmann”

4. Amy Broadmoore presents 10 Children?s Books About Math posted at Delightful Children’s Books, saying, “Here are ten excellent picture books about math. These books are both entertaining and helpful for teaching kids about addition, subtraction, multiplication, division, measuring, fractions, graphing, very large numbers, and roman numerals.”

5. Colleen Young presents Top 100 Tools for Learning 2011 posted at Mathematics, Learning and Web 2.0, saying, “The tools I use from Jane Hart’s top 100” and Top 10 Mathematics Websites posted at Mathematics, Learning and Web 2.0, saying, “Another possibility – not sure which of these posts best for the carnival!”

6. IMACS  presents Alternatives to Math Competitions for the Dreamer Child and An Introduction to Modular Arithmetic posted, saying, “When choosing activities to engage a math-talented child, think about what makes that particular child thrive.”

7. Earl Samuelson of samuelson mathxp’s posterous submitted a bunch

8. Edmundo Gurza presents Writing with LaTex – Cure For Some Headaches posted at Reconstructing Climate.

9. William Dvorak presents Amortized Analysis posted at Deterministic Programming”

And here’s for Geogebra enthusiasts:

John Golden presents 2nd Fundamental Theorem of Calculus posted at Math Hombre, saying, “A GeoGebra activity to better understand functions defined as an integral, as in the 2nd fundamental theorem. Two other Calc 2 sketches at http://mathhombre.tumblr.com/post/11912609932/by-parts-dynamic-text and http://mathhombre.tumblr.com/post/11910861558/by-parts-and-product”

Guillermo Bautista presents  The Pantograph at GeoGebra Applet Central and Sanjay Gulati presents Maximum area of a rectangle inside a triangle at Mathematics Academy.

That’s all for now. See you next time. I think I host every fifth of this math blog carnival since hosting the Math and Multimedia Blog carnival #7.