Patterns and Structure Exhibit

Symmetry is a common example of patterns. For example, the symmetry in our bodies explains the aesthetic value we associate with symmetry as a mathematical concept.

Coming up with a precise definition of symmetry can be a real challenge. But it’s also worthwhile because once we have that idea, we will discover that we can classify symmetries (rotation, reflection, translation…), superimpose them, and use them to distinguish shapes. Not to mention symmetry’s obvious role in art and architecture, and its fundamental role in many branches of physics and chemistry, such as crystallography. Until 50 years ago, it was assumed that all the fundamental laws of physics were the same in space and time. The discovery that this was not true at the atomic level was surprising, raising new philosophical questions about the universe we live in. It suffices to say, this section is a tangible manifestation of the Creator’s creativity.

1) Mirrors – Symmetry

– An object’s symmetry is defined by “transformations that restore the object to its original appearance”.

– A snowflake has 6 rotational symmetries and 6 reflection symmetries (can you find them?)

2) Honeycomb Mathematics – Periodic Tiling

Most of the tiling you see around you (like a bathroom floor or a honeycomb) is periodic tiling that remains unchanged when displaced sideways a certain distance in a certain direction.

3) Is There a Pattern? Lapidary Tiling

You will find it impossible to get a pattern that repeats itself after a lateral displacement.  However, Roger Penrose proved that this tiling may continue to cover the entire surface.

4) Packing Oranges (How to put the most oranges in a box).

This pattern is called “hexagonal” because each sphere has six neighboring ones. It is a two-dimensional pattern because it has one layer and can be drawn in a plane.

Bees discovered this pattern a long time ago and used it to make honeycombs, and while the result is true and intuitive, it is not easy to prove.

5) Take Your Chances! Gauss distribution

In the 19th century, Gauss discovered that when an experiment is repeated too many times, the distribution of results around the mean value is given by a bell-shaped shape.

Although the height and width of the bell depends on the scale, all experiments produce the same Gaussian distribution when repeated many times. This is a mathematical fact, not a physical fact, and does not depend on the nature of the experiment.

6) Dancing Pendulums Chaotic Motion

The behavior of physical structures such as a pendulum is determined by equations with unchanging solutions for certain initial conditions.

If a simple pendulum, for example, is lifted at a certain angle and then released into motion, it always follows the same path. This pendulum motion is so regular that clocks were based on it until recently.

The equations for a rotating pendulum or a magnetic pendulum are very complex. The slightest change in their initial conditions results in large changes in their trajectory, i.e., chaotic behavior.

6) Magnetic Pendulum (Irregular Chaotic Motion)

Meteorologists devised a set of equations to describe the behavior of the Earth’s atmosphere as a way to predict the weather. However, they were surprised to find that even if they always started from the same point, the equations gave divergent predictions in the end. This means that the equations describe a “chaotic” system. This also means that a butterfly flapping its wings in Japan can lead to a hurricane changing course in the Caribbean. Chaos Mathematics has thus become one of the major disciplines.

7) Square Wheeled Bicycle

What makes you think about having square wheels on your car? What routes will you take to reach your goal? Is there a conservation of energy? These and other questions will be answered by the Square Wheel Bike exhibit.

Al-Quds University