Symmetries

MM Pattern

Demetrios Benetos

mm ceiling pattern

Brenda Urena

Photo captured in my living room

Demetrios Benetos

I saw these beautiful mandalas and border patterns during my visit to Dublin Castle a few years ago.

Michael Blaine

Saw this m1 on Lafayette Ave in Astor Place.

Michael Blaine

Again, this mg border pattern I saw near Astor Place.

Michael Blaine

I was walking over to Astor Place yesterday when I saw this 1m border pattern on a lamp post:

Michael Blaine

This is a border pattern I saw down in the Subway.  A 12 pattern, I believe!

Michael Blaine

A type 12 border pattern on 20th St in Manhattan.

Objects with rotational symmetries, which we’ll call “mandalas”, occur in many cultures. The mandala gallery will show some examples.
To celebrate St. Patrick’s Day, here are two Celtic crosses. The first is from the Gallarus Oratory in Ireland, and has symmetry type D4. The second one, which is a Z4, is from Santiago de Compostela in Spain.

The Credit Suisse building (formerly Met Life North) by Madison Square.

I found this Ancient Greek example in the Metropolitan Museum.

You have to start from nothing, enter from the outside and find the gates to ascend to successively higher and more central levels of enlightenment until you are enlightened about the heart of the problem at the center or apex. Why is the Medicine Buddha Mandala particularly apt for this purpose? Can you think of other ways that a mandala is like a math problem?

How does the Mandala of the Peaceful and Wrathful Deities of the Bardo (on the 4th floor) compare, in terms of symmetries, with the others on display at the Rubin? What symmetries does it lack?

Like the 3-dimensional mandala, a first order language is built up from its base, which is its set of symbols. Above the base we build the terms, and on the third and most important level we build the formulas.

Are there higher levels? How could we use the language of mandalas to build up deductions?

What about the semantics?

When we first started learning about the mandalas and the history behind them i was a bit lost and the thought the only reason that we were there was that this might me an interest/hobby of the professor. Although after listening for some time to the tour guide and trying to understand why we were there it hit me. The Mandalas have a lot of messages that they send out through the shapes and colors and forms of the paintings. I think the professor professor was trying to draw the parallel between the languages of Budhism and mathematics. I believe he was trying to make us think outside the box so we would have an easier time understanding the concept of languages as a whole and then we could transition into the language of mathematics easier. It was a smart idea i believe and i think i understood the message. -Denis Buci (Tue and Thu MTH 4315 at 2:55pm- 4:30pm.