Geometry is a branch of mathematics that is used widely in arts. It is one of the methods that people use to…
› Represent their environment. › Interpret ideas. › Create designs or constructions.
The Spiral Ramp at the Vatican? Or the drawing by MC Escher?
Point –A position on a line or in a plane. Line Segment– A line that is bound between two points. Circumference– A closed curve whose points are all an equal distance from a central point. Polygon–A closed shape formed by line segments.
A polygon can be regular… › If it has all equal
sides and angles.
Or irregular… › If the sides and
angles are different.
Transformations are modifications made on geometric forms that maintain the basic characteristics of the form.
Variations in the original form, maintaining the basic values through similarity or proportionality.
Variations in the position, like rotation, reflection, and translation.
Congruent figures are two figures that are exactly the same
Similar figures are two figures that have equal angles but their sides are proportional.
In order to create a similar shape, we can use the technique of enlarging. › All points must move the same direction. › All points must move the same distance. › All angles stay the same. › All lines become proportionally larger.
Next to the polygon, make an external point A. Measure the distance between the point A and the first vertex (point) of the polygon Draw a line from point A that passes through point N. Draw a new point at double the distance from point A.
Draw a small irregular polygon with a ruler like the initial of your name, an animal, a symbol, etc with a minimum of 6 vertices. Use the necessary steps to make the shape double it’s size.
Translation is moving a shape. Every point of the shape must move:
› The same distance › In the same direction
Next to your polygon, draw a 5 cm long “translation line” to act as a guide. Use the ruler to draw equal (5 cm) parellel lines from each vertex. Connect the dots.
Draw a rotation point (R) next to your polygon. Connect the point R with the first vertex O. Place the protractor center at the point R and mark the degrees. In this case, 40º. Measure the distance from the point to the vertex with a ruler and draw a line of the same length through the 40º mark. This is the new vertex O. Repeat.
If we augment the number of sides of a regular polygon, it begins to resemble a circumference.
In order to draw a regular polygon, it can be “inscribed” on a circumference.
A polygon is inscribed when all of it’s vertices touch the circumference without crossing it. INSCRIBED NOT INSCRIBED