|Tangents of Crop Circles|
Tangents of Crop Circles
- Crop circles, formed by crushed crops, are a pattern of geometric shapes, such as triangles, circles, etc. They illustrate many geometric theorems and relationships between the shapes of the pattern.
Comparing three crop circles that aren’t exactly touching can form three tangent lines, with each line adjacent to all three of the circles. Connecting the center points of all the circles creates a triangle, which is equilateral. The circumscribed circle of the triangle includes all the center points of the three circles and shows relations of diameter to these circles.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Geometry
Line k is a tangent touching the edge of all three congruent circles. Line j and l pass through the center of the three circles. The distance from the center of a circle to a point on its edge creates the radius, and all radii (from congruent circles) are also congruent, so the distance between line j and k is congruent to distance between k and l.
Triangle ABE is similar to triangle ACD since it is formed by a parallel line passing through triangle ACD. Line segment AB equals the distance of a, while line AC equals 2a, making the ratio of the two triangles 2:1. Therefore, 1/2BE = CD.
Why It's Interesting
Crop circles are interesting because
- There are currently no teaching materials for this page. Add teaching materials.
About the Creator of this Image
Bert Janssen, an award-winning author and researcher, has written many articles about crop circles due to his interest in geometry, shapes, and forms.
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.