News for Nerds: The soon-to-be-famous DSO Pretzel Logo

About the DSO plate and rotational symmetry, or the odd function....

The soon-to-be-famous "DSO Pretzel Plate" logo is an undeniably elegant and yet down-to-earth artistic creation. Note that our other famous "DSO Coda" (Stylized note to look like a d, followed by the musical symbols dal segno al coda) logo will be discussed at even greater length in future posts. I bet you can hardly wait for that. Have a snack ready for that post - I recommend pretzels! (Aside: merchandise showcasing either logo - or both! - is available via the Shop link on this web site. So shop away! Purchase an item - or perhaps boatloads of items: Stylish shirts, hoodies, ballcaps, tote bags or mugs for your friends, relatives, co-workers.

Ahem ... Carrying on:

It's possible the elegance of the design can be attributed to the mathematical symmetry it holds. At first glance, it does not seem symmetrical, as a simple fold along the y-axis or the x-axis (at value 0) does not yield a mirror-like reflection: Think of a row of trees along the edge of a calm, clear lake and its image in the water. Instead, mathematically, it models an ODD function (much like its creator!).

The stylization of the "D" and the "O" are key contributors to the logo's appeal: Due to the unique design, just like the Sine function: f(x) = sin(x), it has ROTATIONAL symmetry. Spin the plate a full 180 degrees and .. voila ... it is the same! To be clear: Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin; this may be also represented by the equation f(x) + f(-x) = 0 That is, the equation holds for all x such that x and -x are in the domain of f, which can be restated: f(-x) = -f(x) If you graph the so-called "odd function" of f(x) = x(cubed), the rotational symmetry is plain to see. (Look it up!)

In a future post I will discuss the birthing of the pretzel logo in a time of crisis during a pandemic; note that the pretzel pieces are arrange to resemble "DSO" (aka Deservedly So). In case you were wondering. Oh, and ... DSO is just a lazy abbreviation, not an acronym or an initialism (more on that, in future posts, as well! Logos for nerds. You are welcome!