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 Ponziis 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 Daughters - (The Four Colour Conjecture)

15" x 30" Acrylic on canvas, 2010

A plane map can be coloured in at most four colours. The first panel shows that if a map is drawn in one continuous curve starting and ending at the same point without lifting the pen off the paper, then it can be coloured in only two colours. If the continuous curve is drawn so that it starts and ends at different points, then at most three colours will be needed to paint that map - as shown in the second panel. If more than one continuous curve is needed to draw the map (the pen is lifted off the paper), then at most four colours will be sufficient to colour the map - the third panel.

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.