How are Aryavarta, Brahmavarta and Madhyadesa defined?

Question

I believe Aryavarta contains Madhyadesa which contains Brahmavarta.

Where are these defined geographically?

Answer 1

• Brahmavarta lies between the two rivers Saraswati and Drishadvati.

Manu Smriti 2.17. That land, created by the gods, which lies between the two divine rivers Sarasvati and Drishadvati, the (sages) call Brahmavarta

• Madhyadesha

  2.21. That (country) which (lies) between the Himavat and the Vindhya (mountains) to the east of Prayaga and to the west of Vinasana (the place where the river Sarasvati disappears) is called Madhyadesa (the central region).

• And, Aryavarta is the land between Himalayas and the Vindhya mountains.
  

2.22. But (the tract) between those two mountains (just mentioned), which (extends) as far as the eastern and the western oceans, the wise call Aryavarta (the country of the Aryans).

Similar verses from Dharma Sutras of Vashishta:

The region east of where the Sarasvati¯ disappears, west of Kalaka forest, north of Pariyatra mountains, and south of the Himalayas is the land of the Aryas; 9 or else, north of the Vindhya mountains.

10 The Laws and practices of that region should be recognized as authoritative everywhere, 11 but not others found in regions with Laws contrary to those.*

12 According to some, the land of the Aryas is the region between the Ganges and Yamuna. 13 According to others, vedic splendour extends as far as the black antelope roams.

(1.8-13)