Theorems & Constructions
Dragon Curve in Red
Acrylic on canvas, 2013
30" x 26"
Green Dragon
Acrylic on canvas, 2013
24" x 36"
City Dragons
Acrylics on canvas, 2013
36" x 26"
Ice-cream on the Beach
(Abu Wafa Buzjani)
Acrylic on canvas, 2011
24" x 20"
Abul Wafa lived in Buzjan, modern day Iran between 900 and 998. He wrote several treatises on Euclid, Diophantos and Al-Khwarizmi. He is best remembered for the puzzles he created on dissection with the use of only a straight edge and a pair of rusty (fixed opening) compasses. In this puzzle, you have to construct the largest possible equilateral triangle in a given square.
Bubbles in May
(Three Circles through a Point)
Acrylic on canvas, May 2010
24" x 24"
If three circles of equal radii pass through a point, then another circle of the same radius can be drawn through the points of intersection of the three circles.
Sharing a Square
15" x 30" Acrylic on canvas, 2008
How would you share a square pizza between any number of people (3 or 5 shown here) so that everyone gets an equal share of the crust?
Golden Ratio
15" x 30" Acrylic on Canvas
2009
Pascal's Theorem & The Pascal Line
24" x 24" Acrylic on canvas,
February 2010
At the age of 16, Blaise Pascal discovered and published his famous theorem entitled Essai pour les coniques. The theorem states that if a hexagon is inscribed in a conic then the three points in which the opposite sides meet are collinear. The line is The Pascal Line. The above work shows The Pascal Line in a zig-zag inscribed hexagon.
A Form
24" x 24" Acrylic on canvas, 2010
The red rectangle is in the A Form ratio. This construction shows how it can be constructed from a square.
Golden Petals
(The construction of golden sections and the golden rectangle)
20" x 24" Acrylic on Canvas
2009
Abu' Wafa Buzjani's construction of an equilateral triangle in a square.
Abu'l Wafa Buzjani
24" x 30" Acrylic on canvas
2008
Abu'l Wafa Buzjani's problem in Blue and Green
Fermat Point
Acrylic on canvas
20" x 24"
To Divide a Line
Acrylic on canvas
20" x 30"
Pythagoras
Acrylic on canvas
24" x 30"
Monge's Theorem
Acrylic on canvas
18" x 24"
Double or Nothing
Acrylic on canvas, 2009
30"x 30"
Holditch
Acrylic on canvas, 2008
18" x 24.5"
The Holditch curve is generated by a fixed point on a chord of a curve as the chord moves around a convex curve.
Sacred Cut
Acrylic on canvas, 2010
24" x 30"
The Sacred Cut was perhaps historically used to find a method to double the area of a given square. For example, in order to double the altar they could not simply double the sides. The Sacred Cut gave a means to do it. It produces the Silver Rectangle with ratio of sides 1:√2 which is used in A Form paper. This work illustrates how to construct the Silver Rectangle or the Sacred Cut and also gives an impression of doubling both the rectangles and the squares.