1. Art History Special: Geometry and Art
Mandalas

2. Timeline
The circle has been symbolic to many cultures through history. It was as early as the 8th century that the mandala may have been used in Tibet as an aid to meditation.
Mandala
Tibetian Painted 19th century Tibetan mandala of the Naropa tradition, Vajrayogini stands in the center of two crossed red triangles, Rubin Museum of Art. Image in public domain. 

3. What is it?
A mandala (Sanskrit for “circle”) is a geometric design that is used symbolically and ritually in some religions, particularly Buddhism and Hinduism as well as in some Native American cultures.
Mandala
Hindu mandala. (Yantra) Released to public domain by Nharipra through Wikimedia Commons

4. Mandala What’s it used for?
Mandalas often contain images of religious deities such as Buddha or other figures. It is believed that their purpose is to aid in meditation and perhaps, inspire visualizations.
Mandalas are also used sometimes in psychotherapy. In Tibetian Buddhism they are used for healing.
Some people believe that mandalas help create wholeness and unity.
Mandala
17th century art from Indian manuscript. Public Domain

5. Mandala Sand Painting Sand Mandalas
Below are links to two interesting videos showing Buddhist monks doing sand painting of mandalas.
Israeli Sand Paintings : website showing a large variety fo sand painting of mandalas and other mandalas
Mandala
Photo of a Chenrezig Sand Mandala created and exhibited at the House of Commons on the occasion of the visit of the Dalai Lama on 21 May GNU free license at Wikimedia granted by Colonel Warden, photographer.

6. Tibetan Buddhist thangka painting of a mandala, 19th century
Tibetan Buddhist thangka painting of a mandala, 19th century. Public domain through Wikimedia

7. Window of Marsh Chapel at Boston University John Stephen Dwyer photograph, Wikimedia Creative Commons ShareAlike 3.0 license

8. 1900. Painting of Mahavira. Public Domain image photographed by Jules Jain, Wikimedia Commons.

9. Public domain image, Painted 17th century Tibetan 'Five Deity Mandala', in the center is Rakta Yamari (the Red Enemy of Death) embracing his consort Vajra Vetali, in the corners are the Red, Green White and Yellow Yamari, Rubin Museum of Art

16. Examples
Link Above: Short video showing a mandala being drawn.
Link Below: Longer video showing a large variety of mandalas and mandala type art.
Mandala
Tibetian. Kalachakra thangka painted in Sera Monastery, Tibet. Released into the public domain by Kosigrim through Wikimedia