Mathematics in Art Course: Some Euclidean geometry without constructions and Examples of Stencils and Templates (Randon Geometric Shapes that are either Symmetrical or Asymmetrical)

When Viewing Examples of Student Work:

Often a single example of work may not demonstrate all the required objectives for a particular assignment. Instead students should collectively consider: the required objectives for each assignment, the multiple examples presented on this website and during in class presentations. As well ideas discovered through a student's independent research in combination with various examples and ideas presented by instructor will ultimately be the best approach for synthesizing ideas and reaching the requirements (and unique outcome) for any particular course project. Attendance and participation in all classes and meeting with instructor with Art Assignments in progress well in advance of deadlines will increase chances for desired grade. To access all posts and links for the art part of this course go on the right side of this course website."LISTINGS FOR LECTURES (COURSE TOPICS) & ASSIGNMENTS"

Clarification of Euclidean geometry without constructions and Examples of Stencils and Templates

Euclidean geometry without constructions:
In addition to this information below also see on line information regarding Geometry that Relates to Euclidean Constructions from the the art website here:
http://derekbruecknermathinartcourse.blogspot.ca/2014/12/euclidean-constructions-and-euclidean.html

As discussed and presented in class numerous times, Euclidean geometry without constructions is a minor point regarding art assignment 1 and just means random two-dimensional geometric shapes that do not require the mathematical constructions. http://en.wikipedia.org/wiki/Geometric_shape (Hopefully this wikipedia link should clarify for people what Euclidean geometry without constructions means with the examples of 2D geometric examples presented in the link)

Most two-dimensional geometric shapes can be defined as a set of points or vertices where lines connect the points in a closed chain. Such shapes are called polygons and include triangles, squares, rectangles, hexagons, octagons and even a golden ratio construction of a pentagon is technically a geometric shape. Other shapes may be bounded by curves (arcs) such as the circle or the ellipse.

A geometric shape could also include points joined by a combination of straight lines and arcs as well as demonstrated by the following sequence of purple and orange lines connecting points together.

To further investigate and explore possibilities with this geometric shape the next images demonstrate further possibilities of the shape presented as a combination of solid form and line and finally concluding as a solid shape.

As presented here, Geometric Shapes are not exclusively symmetrical, geometric shapes which are not symmetrical could also be created by joining a set of points by using lines and or arcs to join the points together in a closed chain.

These Mathematical concepts and Euclidean geometry without constructions can be depicted using solid colour to fill in the shape(s) or they can be depicted using various coloured lines. In the examples of colour outlined shape the viewer can see previous layers of other shapes and math concepts behind the colour outlined shape.

Here are some examples below of stencils and templates cut into 2 -dimensional geometric shapes most of these examples below are not symmetrical