What you are seeing is a growth pattern of sticky notes that uses the Golden Angle (137.5 degrees) and then slowly decreases. This angle is commonly found in the plants all around us because it is an optimal angle for growth.
It was a lot of fun playing with the growth angle while creating memorizing spirals in this code, so I created a version for everyone to play with (see below):
There is lots of fun to discover here. The fractal starts using the Golden Angle of Phi (137.5) and then decreases. You will find interesting behaviors when the angles approach numbers that divide into multiples of 360 more easily (40, 45, 60, 90, 120, 180, etc…). I wanted to do so much more, but had to stop somewhere.
If you want to know more about Phi, many mathematicians and creative types have presented it better than I (see below):
Poetry forms are like a puzzles. You have to take the words you want to say and rearrange them, find synonyms, and reformulate them until they can fit in a form. This problem solving is so similar in math.
One of the first forms to play with is the Haiku. It is a three line poem with no rhyming scheme that fits a syllable pattern of 5/7/5. Traditionally there is a season mentioned (Kigo) and a cutting word to compare two ideas (Kiru). Learners can try to do a traditional Haiku, or they can just work with the syllable pattern to start. This can be done in any classroom to contemplate the concepts that are being learned in a different way. When we relate these abstract ideas to our inner beings, we remember.
Once poems are complete, maybe a work of art can complement it.
This week learners can dive deep into their imaginary worlds (or real world inventions). The project this week is to create a map, castle, spacecraft or invention. The math focus will be on developing a sense of scale. Younger learners may practice scale with proportions in their drawings. Older learners may add units and measurements to their designs.
Offer various materials for their designs: graph paper, extra large sheets, engineering papers, isometric, or hex. Facilitators can supplement learning by looking at maps, blueprints, and patent designs that learners are interested in.
Start with a compass or protractor and create a circle with evenly spaced points around it. Students can figure out how many degrees need to be between points (example: if you want 10 points, then there are 36 degrees between each point, for 9 points : 40 degrees, etc.)
Draw your circle and points on a board
Place pins or nails in your board
Wrap string in various patterns and see what emerges.
Students can study remainders (mod functions), multiplication, and sequences.
Star patterns, secondary polyhedra, and cardioids may emerge.
If you don’t have wood and nails, then this can be done on paper with a pencil and ruler or sewing with string on paper.
Encourage students to look at other shapes, axese, or lines and create works of art. (boards can be painted, multiple colors and thicknesses of string can be used, and students can contemplate 3-dimensional approaches for this art (like with dowels).
I sometimes feel like a broken record. I repeat so much in conversation with parents, educators, and students when I consult with them on learning math that finally I sat down and brainstormed a website to share my ideas and best practices that I have used through the years. My plan is to share my stories, syllabuses, games, reviews, poetry,… the list goes on. I look forward to what this grows into. As a reader, please let me know what would be helpful and what you’d like to see here.
This week I created a logo, posted my Marie’s Atlas books here for free (It’s been 5 years since I wrote the first book!), and organizing all of my materials for web content. I am still pondering if I should go by grade or concepts or age for organizing materials. I homeschool my own children and find that Grade is meaningless, but concept or levels of math are not.
I am also trying to be able to earn as a tutor/artist/author without setting up paywalls, annoying ads, or seeming pushy. For now I have decided to use affiliated links and donate buttons. This way if people can and want to pay for content, they can.
I hope Fractal Kitty will help make math fun and meaningful for many. Thanks for support and please subscribe.