Short answers, pulled from the story.
The earliest known pointed arch emerged from the Bronze Age ruins of Nippur before 2700 BC. This structure predates the birth of Christ by nearly three millennia and represents the first known use of the form.
Architects in Samarra experimented with the four-centred arch by the 9th century to achieve greater height and a sharper apex. This evolution is documented through changing proportions in Qusayr Amra, Hammam as-Sarah, and Qasr Al-Mshatta.
Builders in Sicily, England, and France used the pointed arch to create the rib vault between 1135 and 1490. This system liberated walls from heavy stone roofs and allowed for thinner walls and massive stained glass windows.
The equilateral arch is derived from a triangle where the span of the arch equals the arc radii. Stone cutters used this design to represent the Holy Trinity through its three equal sides.
The Tudor arch became a hallmark of the Tudor dynasty from 1485 to 1603 in England. This low and wide variation of the four-centred arch appeared in palaces, churches, and public buildings.
Horace Walpole initiated the resurgence at Strawberry Hill House in Twickenham, London, beginning in 1749. The style expanded to the British Houses of Parliament between 1840 and 1876 and the Gothic train station in Peterhof, Russia, completed in 1857.