Birch bark manuscripts are documents written on pieces of the outer layer of birch bark, which was commonly used for writing before the mass production of paper. Evidence of birch bark for writing goes back many centuries and appears in various cultures. The oldest such manuscripts are the numerous Gandhāran Buddhist texts from approximately the 1st century CE, from what is now Afghanistan. They contain among the earliest known versions of significant Buddhist scriptures, including a Dhammapada, discourses of Buddha that include the Rhinoceros Sutra, Avadanas and Abhidharma texts.
Sanskrit birch bark manuscripts written with Brahmi script have been dated to the first few centuries CE. Several early Sanskrit writers, such as Kālidāsa (c. 4th century CE), Sushruta (c. 3rd century CE), and Varāhamihira (6th century CE) mention its use for manuscripts. The bark of Betula utilis (Himalayan Birch) is still used today in India and Nepal for writing sacred mantras. Russian texts discovered in Veliky Novgorod have been dated to approximately the 11th to 15th centuries CE. Most of those documents are letters written by various people in a local dialect, Old Novgorodian. The Irish language's native writing system Ogham, sometimes called the "tree alphabet", was traditionally attributed to the god Ogma who wrote a proscription on birch to Lugh, warning him; the text of this proscription can be found in the Book of Ballymote. The first letter of Ogham is beith; beithe means "birch".
A Hindu temple, also known as a Mandir, Devasthanam, Pura, Kshetram or Kovil, is a sacred place where Hindus worship and show their devotion to deities through worship, sacrifice, and prayers. It is considered the house of the god to whom it is dedicated. Hindu temple architecture, which makes extensive use of squares and circles, has its roots in later Vedic traditions, which also influence the temples' construction and symbolism. Through astronomical numbers and particular alignments connected to the temple's location and the relationship between the deity and the worshipper, the temple's design also illustrates the idea of recursion and the equivalency of the macrocosm and the microcosm. A temple incorporates all elements of the Hindu cosmos—presenting the good, the evil and the human, as well as the elements of the Hindu sense of cyclic time and the essence of life—symbolically presenting dharma, artha, kama, moksha, and karma.
The spiritual principles symbolically represented in Hindu temples are detailed in the ancient later Vedic texts, while their structural rules are described in various ancient Sanskrit treatises on architecture (Bṛhat Saṃhitā, Vāstu Śāstras). The layout, motifs, plan, and the building process recite ancient rituals and geometric symbolism, and reflect beliefs and values innate within various schools of Hinduism. A Hindu temple is a spiritual destination for many Hindus, as well as landmarks around which ancient arts, community celebrations and the economy have flourished.
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava. The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometrywas further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.
Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form. The oldest extant mathematical document produced on the Indian subcontinent is the birch bark Bakhshali Manuscript, discovered in 1881 in the village of Bakhshali, near Peshawar (modern day Pakistan) and is likely from the 7th century CE.
Utpala, also known as Bhaṭṭotpala (Bhaṭṭa-Utpala) was an astronomer from Kashmir region of present-day India, who lived in the 9th or the 10th century. He wrote several Sanskrit-language texts on astrology and astronomy, the best-known being his commentaries on the works of the 6th-century astrologer-astronomer Varāhamihira.
Pancha-siddhantika (IAST: Pañca-siddhāntikā) is a 6th-century CE Sanskrit-language text written by astrologer-astronomer Varāhamihira in present-day Ujjain, India. It summarizes the contents of the treatises of the five contemporary schools of astronomy (siddhantas) prevalent in India.