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Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [ 1 ] [ 2 ] Heronian triangles are named after Heron of Alexandria , based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84 .
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
This formula is the same as Heron's formula, proved by Heron of Alexandria about 60 BCE, though knowledge of the formula may go back to Archimedes. As precipitation was important agriculture and food production, Qin developed precipitation gauges that was widely used in 1247 during the Mongol Empire / Southern Song dynasty to gather ...
The Class VIII (ages 12–13) book (Punjab Textbook Board) on Islamic Studies reads: "Honesty for non-Muslims is merely a business strategy, while for Muslims it is a matter of faith." The Class V (ages 9–10) book (Punjab Textbook Board) on Social Studies says: "Religion plays a very important role in promoting national harmony.
The Punjab emerged as an important agricultural region, especially following the Green Revolution during the mid-1960s to the mid-1970s, and has been described as the "breadbasket of both India and Pakistan." [3] Punjab's history is a tapestry of conflict, marked by the rise of indigenous dynasties and empires.
Punjabi culture grew out of the settlements along the five rivers (the name Punjab, is derived from two Persian words, Panj meaning "Five" and Âb meaning "Water") which served as an important route to the Near East as early as the ancient Indus Valley civilization, dating back to 3000 BCE. [1]
Punjabi literature, specifically literary works written in the Punjabi language, is characteristic of the historical Punjab of Pakistan and India and the Punjabi diaspora. The Punjabi language is written in several scripts, of which the Shahmukhi and Gurmukhī scripts are the most commonly used in Western Punjab and Eastern Punjab, respectively.