The golden ratio has spawned a beautiful new curve: the Harriss spiral | Alex Bellos

Abstraction: Edmund Harriss discovers branching Harriss spiral from plastic number rectangle

Key points:

• Harriss found the rectangle that subdivides into two similar rectangles and one square; its aspect ratio is the plastic number ~1.32472
• Adding quarter-circle arcs to each square in the recursive subdivision produces a branching spiral (the Harriss spiral)
• The plastic number (1.32472...) was previously known in mathematics but no one had drawn the associated spiral
• Harriss generalized to "proportion systems": rectangles subdividing into only squares and similar rectangles; 3 options for 2-piece, 16 for 3-piece
• The ratios produced by proportion systems are algebraic numbers; Harriss conjectured every algebraic number appears as such a ratio
• Motivation: extend the golden ratio into a wider family of mathematically and aesthetically meaningful proportion systems

Connections: Edmund Harriss · Geometry · Golden Ratio · Mathematical Art

Source: http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral?CMP=share_btn_fb