The artistry of quilt geometry can be demonstrated with something as simple as well placed squares. I love black and white quilts with a highlight of red. Now, if this had been my quilt, I might have put one small bright yellow square in the mix, but that's me. I've made a lot of quilts made artistically of just squares, and several that were black and white and red (with that one tiny bit of yellow.)
Most pieced quilts are made up of combinations of squares, rectangles, and triangles. This sampler is a good example of what those combinations can create.
When you have pieced squares, they can be softened by the use of circles in the quilting stitches. I've tried quilting circles and not been very successful myself. I am a machine quilter--the carpal tunnel and a bit of arthritis will not let my hands cooperate with hand quilting.
Putting those basic shapes together as in the sampler and the squares and quilted circles above is wonderful. But one of my favorite things to do is create an illusion, as this quilter did, of circles using the squares, rectangles, and triangles.
Quilts are history as well as geometry, that block in the center is called 54-40 or Fight--commemorating the slogan of James Polk in his 1844 Presidential Campaign.