Curiosities
Lily pads, 2020
Acrylic on canvas, 30"x24"
My mother has a lily pond for fish, frogs, snails, snakes and other creatures who live in a circle of life in her garden. When frogs leap into the pond they cause circular ripples in the water, sometimes splashing drops onto the lily pads.
Non-intersecting circles can be arranged in 1, 2, 4, 9, 20, 48, 115, 285,…ways. Here five circles are arranged in the 20 possible ways.
Families I,II,III & IV (Blue Moon)
Acrylic on canvas, 2018
Families VI(i), 2020
acrylic on canvas 48" x 22"
Families VI(ii), 2020
acrylic on canvas, 48" x 22"
Sam Loyd's Muse, 2012
Acrylic on canvas 36” x 30”
Sam Loyd and Henry Ernest Dudeney were self taught mathematicians who lived in the last century and made a living as puzzelists by creating and selling their puzzles to magazines etc. Sam Loyd was American and Henry Dudeney lived across the Atlantic in the England. They were contemporaries and rivals. Sam Loyd was the more successful of the two being pushy and charismatic while Dudeney was the more elegant mathematician. Sam Loyd was also an excellent chess player and created several chess puzzles. The Chessboard Disarray is a work inspired by one of Sam Loyd’s puzzles and the Ponzi is a homage to one of Henry Dudeney’s best known dissection puzzles.
This work presents the solution to a dissection puzzle of Sam Loyd’s which he called “The Trapezoid Puzzle”. The problem was to divide a square into five different parts so that all five pieces could be put together to form a square, a rectangle, a triangle, a parallelogram and an orthodox Greek cross.
Lady Ponzi
(Dissection of an equilateral Triangle - Dudeney)
Acrylic on canvas
24" x 30"
Perfect
Acrylic on canvas, 2012
28" x 16"
Some numbers are Perfect. If the sum of all the factors (divisors) of a number is equal to the number i.e, 6 (1+2+3) or 28 (1+2+4+7+14), they are said to be perfect. Perfect numbers quickly grow very large. The 3rd Perfect Number is 496 (1+2+4+8+62+124+248) and the 4th is 8218. This work proclaims 28.
Chessboard Disarray
Acrylic on Canvas, 2010
18" x 24"
This was inspired by the puzzle MAKE IT SQUARE which runs like this: "This design contains exactly sixty-four little squares, and the puzzle consists in showing how it may be cut into the least possible number of pieces to make a large eight by eight square, with the pattern preserved." The original puzzle is most probably one of Sam Loyd's puzzles.
Three Sisters, 2010
15" x 30" Acrylic on canvas
Cartographers knew, from experience, that a 2D map could be coloured in a maximum of 4 colours so that no two adjacent areas had the same colour. It took mathematicians very long to prove that this was true. It was one of the first major theorems to be proved with the help of a computer.
Each sister draws her own type of map.
Magic Square
Acrylic on paper
2009
4x4 Dice Roll
(Inspired by Erik & Marty Demaine rolling inside a die)
30" x 30" Acrylic on Canvas
2009
3x3 Magic Square
Acrylic on canvas
Chessboard Rearrangement
Acrylic on canvas
The Great Monad in two Horshoes
Acrylic on canvas
16
Acrylic on canvas
24"x24"
The sum of the perpendiculars to the sides of an equilateral triangle from a point within it is constant. For this triangle that sum is 16. Hence the name. You can measure it by counting the heights of the small equilateral triangles.