A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. G. H. Hardy
But, I digress. Back to the essay, A Mathematician's Lament. Imagine a world in which all students must learn music — not to play an instrument or listen to beautiful compositions. They study the language of music, day in and day out (music theory, notation, transposition, chromatic scales, etc.) without having a clue about how lovely music sounds. Imagine art classes that lack tubes, paper, brushes. Instead, they have worksheets asking students to name the colors and state how to produce them from primary colors. In high school, they get to paint by numbers to prepare them to major in visual sciences that lead to a career.
If you have a hard time imagining such a ridiculous world, read the first three pages of the lament. I double dog dare you!
To scaffold you in playing with patterns, here is a gift. Graph paper with cells of unusual shapes. Of course, if you are bored to death in math class like poor Vi, feel free to doodle. You might discover something.
Feel free to download and print PDFs of the staggered square, triangle, hexagon, and rhombus graph paper. If you like your design, scan it and post it to your blog (or send a copy to me). I would love to start a math creativity gallery.