# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### COMPASS ART 5: More Fun with Euclid

(October 15, 2015)  I showed the students a bunch of pictures of basic mandalas.1  People were intrigued, but alas not all intrigued by the same style.   SECTIONING CIRCLES EUCLID’S WAY One thing that all of these mandalas had in common, though, is that they start out with construction of a circle which is then divided into equivalent sectors.   How…

### COMPASS ART #3 and 4: Fun with Euclid

(October 1 and 8, 2015) I’m combining 2 sessions into one report,  mathematical conversation topics  grouped by how they went over with the students. LAME Compasses: Some students are struggling with their (and my) compasses.  Parts get lost.  Positions slip.  The leads get lost.  No one agrees on which compass model (and we have about 8-10 of them in class)…

### COMPASS ART 1: Intro to Geometry

(September 17, 2015)  Our new math circle course on compass art for 9-11 year olds began with a switcheroo activity:  I gave everyone a printout of an image, and about every 30 seconds said “switch!”  I asked them to pass their page clockwise one person.  The images included: Mandalas from various traditions (Celtic, etc), Zarah Hussein’s Islamic art, Native American…

### Fibonacci

What are the numbers in the Fibonacci sequence? What’s the difference between a sequence and a series? Is it still the Fibonacci sequence if you start with a different first number (or two)? What phenomenon in nature prompted Fibonacci to study these numbers? How is the first number in a sequence determined? What is that first number called? How do…

A Math Circle is, by definition, a conversation about math.   “How many points should our polygon have?” R asked G. They were playing with the dynamic geometry software Geogebra* before today’s Math Circle began. As I was setting up, I had mentioned to them that I hadn’t yet found an obvious way to insert a diameter into a circle…

### The Perfect Circle, the Perfect Rock, the Perfect Perpendicular Bisector

Interesting. Surprising. True.   “Well, we don’t want to waste erasers here in Alexandria, so this is the best method,” argued R (playing the role of Euclid), after she demonstrated how to perpendicularly bisect a line with only a ruler, a straightedge, and a piece of chalk. She faced off in debate against characters who might have different perspectives on…

Geometry is not just the basis of language, but is a language in itself.   “Oh no, now she’s going to ask us the definition of the word flat,” said Z, after the whole group had agreed that a plane can be defined as a “never-ending flat surface without thickness.” I asked, “But aren’t you asking yourselves what flat means?” and the…

### The Point, the Death of Galileo, and a Singing Bowl

People enjoy math from many different pathways.   “I worked on my Flower of Life at home,” said Z as the students entered the room. As she showed me her work, the others began to draw compass designs long before our circle officially began. I unwrapped a tantalizingly mysterious object, and asked for surmises on its identity. When G guessed…

### Attempting the Flower of Life

Some things in math we choose to believe even though we can’t know for sure. Michaelangelo, Bernini, Lloyd Wright (or, the students wondered, was it simply Wright?), Zarah Hussein, Native American geometry designs, mapmakers art, the feng shui compass, and a photo of a piece of jewelry covered the table as the students tried to figure out what the pictures…