Curvilinear shapes are shapes formed entirely from curved lines. Traditional shapes such as the circle and the oval are examples of curvilinear shapes. Alternatively, any sort of shape that has a continuous curved outline can be classed as a curvilinear shape, no matter how unsophisticated it is. Curvilinear shapes could be considered to be the 'opposite' of polygons, which are shapes that consist of entirely straight edges.
- Do curvilinear shapes truly exist?
Many scientists and theologians believe it is in fact impossible to create a perfectly curvilinear shape. They think that if magnified to a sufficient degree, all shapes would be revealed to be consisting of very tiny straight lines. To understand this reasoning, consider the regular hexagon shape along with the regular octagon shape. It is clear that the octagon is more 'circular' than the hexagon, as the octagon has more sides - and if the two shapes were of a similar size, the lines of the octagon would be shorter than those of the hexagon. If we continued this pattern with shapes of even more sides, eventually the shape would very much look like a circle, and only close examination would reveal its true polygon nature. For this reason many think that all curvilinear shapes are in fact polygons with very short sides.
- Geometry: Learning about shapes
Geometry involves learning about shapes. At a very basic level, children are taught to recognize and name different shapes, and think about the number of sides and edges regular 3D shapes have. Many of us believe that the study of shapes stops there - but in fact, there are many other interesting elements about shapes to be discovered. For instance, much can be revealed by drawing a chord on a circle, and then constructing a triangle. As long as the final edge of the triangle remains attached to the circle, interesting angle similarities are produced.