Twenty years were spent in erecting the pyramid itself: of this, which is square, each face is eight plethra, and the height is the same; it is composed of polished stones, and jointed with the greatest exactness; none of the stones are less than thirty feet." -Heroditus, Chap. II, para. 124.
A plethra is a measurement used in Ancient times, equal to 100 Greek feet
See the symmetry in the wings of the butterflies.
The holes in radiolarian and diatom shells respectively exist for differing reasons. Both types of skeleton are formed from silicon compounds. In diatoms, the holes collectively take on the role of a sieve, a two-way filtration mechanism across which water and nutrient molecules permeate the cell.
Just think about a spider's web. That is a complicated geometric design. And it is created, usually, in a perfect manner. Even though I majored in Drawing and Painting in college, and even though I am a Graphic Artist at work, I could not draw a design that perfectly, freehand. Yet a spider, using only his body, continually creates geometrically complex advanced shapes that few, if any, human adults could perfectly duplicate, without the aid of machines, or tools such as a pencil and ruler .and even with a pencil and ruler, it would be very complicated, and possibly even impossible, for most people to exactly duplicate. (by Jeff Jenkins)
What geometric aspects do you see in each spider web?
You can find geometry in many more things in nature. Look around and see what you can find. You will be amazed!