More mirror curves for Physics classroom
Madhuri Bapat, Physics Instructor, Eastern Arizona College, Thatcher, AZ
Followings are nine possible mono linear mirror curves [1] drawn by first drawing 5 x 5
square dot matrix. Besides using them as an activity to reemphasize the laws of reflection
as mentioned in my article in The Physics Teacher of November 2009; they can also be
used to teach symmetry properties. All mono linear Eulerian paths can be mirror curves
but not all mirror curves happen to be symmetric. Here all 9 designs show symmetry
properties. Out of 9 designs, 8 designs (Fig 1 to 8) have a four fold rotational symmetry,
and one design (Fig 9) has a two fold rotational as well as vertical and horizontal
reflective symmetry.
Fig 1
Fig 2
Fig 3
Fig 4
Fig 5
Fig 6
Fig 7
Fig 8
Fig 9
I like to thank Dr. Darrah Chavey from Mathematics and Computer science Department,
Beloit College, Wisconsin; for providing me a copy of Kolam designs book ‘Rangavalipart 10’ by B. P. Bayiri, published in 1986. Above designs are from collection of 35
designs based on 5 x 5 dot matrix.
[1] P. Gerdes; Geometry from Africa: Mathematical and Educational Explorations.
Washington, D.C. Mathematical Association of America, 1999.
More mirror curves for Physics classroom
Madhuri Bapat, Physics Instructor, Eastern Arizona College, Thatcher, AZ
Followings are 5 x 5 dot matrices inside a box. In addition to the plane mirrors
inside of the walls, there are plane mirrors that reflect from both sides are places between
the dots. Imagine a ray of light enters the box at 450 as shown and gets reflected by the
mirrors till exits the box at the same point it enters. The mono linear design it creates is
called Kolam from south India or Sona from Angola, Africa.
Fig 1
Fig 4
Fig 7
Fig 2
Fig 5
Fig 8
Fig 3
Fig 6
Fig 9