A dodecagon is then drawn using the mid-points of the square and the points where the triangles meet.
Four equilateral triangles are drawn from the dodecagon to the four vertices of the square.
Now carry on with the third paragraph: Polygons are named according to the number of sides, combining a Greek root with the suffix -gon, e.g., pentagon, dodecagon
. The triangle and quadrilateral are exceptions.
Here we give steps for building the planters from a smoothsided square to dramatically textured dodecagons
like the one shown in our cover photograph.
From equilateral triangles to squares, regular hexagons, octagons, dodecagons
, parallelograms, regular pentagons, golden rectangles, and more, geometry students will get a hands-on appreciation for the laws that govern these shapes and the opportunity to internalize basic mathematical principles in more than one way.
Students found trapezoids, diamonds, pentagons, hexagons, octagons, nonagons, decagons, dodecagons
, and stars without prompts other than "Find other polygons." Their depth of understanding of shape names was revealed, as were misunderstandings and misconceptions when students labeled the shapes.
The clues are also to be found in derelict Belgian frontier forts with their glacis and redoubts and star-shaped dodecagons
; in the once fashionable spa of Marienbad, with its broken gutters and boarded up windows; in the disused Ladies' Waiting Room of Liverpool Station; the monumental architecture of the bourgeois age, like Brussels' Palace of Justice, whose dimensions "...
The researchers suggest that the nickel and chromium atoms are arranged in a network of incomplete 12-sided figures (dodecagons
) resulting in a "crystalloid" state that falls somewhere between the orderliness of a regular crystal and the completely disordered amorphous state.
The general format used in this activity could easily be extended to an exploration of regular polygons for which students are not likely to have concrete manipulatives, such as heptagons, nonagons, decagons, and dodecagons
. This type of investigation could extend to considering the relationships of the area of polygons to the length of the sides as the sides double or triple.