Curiosities

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 3^rd Perfect Number is 496 (1+2+4+8+62+124+248) and the 4^th 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.