They provide, states Kim Plofker, what in modern mathematical terminology would be called "area preserving transformations of plane figures", tersely describing geometric formulae and constants. Five śulbasutras have survived through history, of which the oldest surviving is likely the "Baudhayāna śulbasūtra" (800-500 BCE), while the one by Kātyāyana may be chronologically the youngest (≈300 BCE). Śrauta rituals and ceremonies refer to those found in the Brahmana layers of the Vedas. These include rituals related to fire, full moon, new moon, soma, animal sacrifice, as well as seasonal offerings made during Vedic times. These rituals and ceremonies in the Brahmanas texts are mixed and difficult to follow. A clearer description of the ritual procedures appeared in the Vedanga Kalpa-sutras. The Vedic rituals, states Burde, can be "divided into Śrauta and Gṛhya rituals". Śrauta rites relating to public ceremonies were relegated to the Śrautasutras, while most Vedic rituals relating to rites of passage and household ceremonies were incorporated in the Gṛhyasūtras (literally, homely; also called "Laukika" or popular, states Lubin). However, the Gṛhyasūtras also added many new non-Śrauta ceremonies over time. The śrautasūtras generally focus on large expensive public ceremonies, while gṛhyasūtras focus on householders and saṃskāras (rites of passage) such as childbirth, marriage, renunciation and cremation. The śrautasūtra ceremonies are usually elaborate and require the services of multiple priests, while gṛhyasūtra rituals can be performed without or with the assistance of a priest in the Hindu traditions. The Śrauta rituals varied in complexity. The first step of a Śrauta ritual was making of an altar, then the initiation of fire, next of Havir-yajnas recitations, then offering of milk or drinkable liquid drops into the fire, then prayers all with mantras. More complex Śrauta rituals were based on moon's cycle ("Darshapurnamasa") and the seasonal rituals. The lunar cycle Śrauta sacrifices had no animal sacrifices, offered a "Purodasha" (baked grain cake) and "Ghee" (clarified butter) as an offering to gods, with recitation of mantras.