1. Architecture of the Roman Empire

2. One of the purposes of Roman architecture was to show their strength and might, the Roman’s hold over its vast empire. The structures were massive and innovative, making use of new technologies, such as the dome, and new materials, such as concrete. The design of many of today’s buildings, especially governmental and civic buildings, have been based on Roman structures, and the architectural innovations of the Roman Empire, such as the arch and the use of concrete, are still present today.

3. The Arch, the Dome, and Concrete Architectural innovations of the Romans

4. The arch became a basic feature in Roman architecture, seen in the arcading of the Colosseum and the expansive property of the aqueducts, as the arch could span a great distance with great stability due to the balance of compression and tension of its structure. The arch could be made by using a variety of materials, such as brick, stone or concrete. Concrete was a new building material made from lime, sand, water, and stones, rock or pottery combined with volcanic stone to delay drying time. Concrete didn’t require specialized workers, whereas stone could crack or break (more expensive medium). Concrete revolutionized architecture, Romans could now mold their space.

5. To hold up to this, the lintel had to have a very strong shear strength, or resistance to being broken off on a plane parallel to the force. The only way to make a stone lintel stronger was to make it thicker. The result was that, of all the pieces of a building, the lintel stones were often the largest and most expensive.

6. Arches redistribute the weight of the load they're bearing. Instead of all that force resting on two points, the force is spread over a larger area. The force is also passed from stone to stone, all the way down to the posts. Thus, rather than depending on the shear strength of stone, the arch depends on its compressive strength, or how well it holds up to being crushed. While stone's shear strength is negligible, its compressive strength is excellent.

7. ARCH

8. By extending the arch it becomes a barrel vault. By intersecting two barrel vaults perpendicularly, a cross or groin vault occurs.

9. By rotating the arch 360 degrees on its axis, a dome is formed.

10. The Romans may have led the ancient world in the fields of art and architecture and made significant contributions to geometry and astronomy, but they contributed little to mathematics. The magnificent construction projects of the Romans may reflect a high level of mathematical intellect but this is not supported by historical evidence. Mathematics in education was often frowned upon, it must have been taught where it was necessary. The low opinion of Mathematics is probably due in part to the professions which required mathematical or scientific learning. These professions were generally considered 'illiberal' and were looked down on. Those requiring an advanced level of Logic, Rhetoric and Oratorio were far preferred.

11. The earliest chord table that survives is in Claudius Ptolemy’s astronomical masterwork, the Almagest (A.D. 140). The chord is close to the modern sine, since Crd τ = 2sin (τ/2)in a unit circle

13. The dome of the Pantheon is the largest from antiquity and was the largest dome in the western world for approximately 1300 years until the early 15th century when Brunelleschi built the Duomo in Florence. The height of the dome, approximately 139 feet (some sources list as 141 feet), is the same as its diameter, forming a sphere in its negative space. The Pantheon was meant to be entered from the front, and in antiquity, a welled courtyard was constructed in the front to funnel visitors through the portico. Once through the large, Greek styled portico, the grand effect of the domed interior would then be revealed. Today, the wall is gone, and visitors can walk around the massive, cylindrical exterior. The dome of the Pantheon was formed by using concrete. To reduce the weight as well as to accentuate the design, coffers were used, creating a honeycomb pattern made by inserting wooden plates into the concrete and removing them once the concrete was dry. An oculus, or eye, of 30 feet in diameter allows light to filter in. The oculus is the only source of light, and is said to symbolize the sun.

15. The Colosseum

16. The Colosseum is set at the southeast end of the Forum, and was the largest permanent arena, or amphitheater built in Rome. (Others were built, though they were temporary ones made from wood.) An amphitheater means “double theatre.” It is an elliptical shape, and is approximately 615 by 510 feet in diameter. It stands approximately 160 feet high, and has four floors. The first three floors on the façade have eighty arches with columns in the Tuscanic, Ionic, and Corinthian order (respectively, corresponding to the sequence of invention). The top floor had consoles that supported posts onto which awnings would be stretched to shield the audience from sun and rain.

17. 1) Doric2) Ionic3) Corinthian

18. There are five orders of columns The Greeks developed the Doric order, the Ionic order, and the Corinthian order. Romans added to these orders by incorporating the Tuscan order and the Composite order, both hybrids of the Greek orders. 1.The Tuscanic is an Italic version of the Doric; where they have a base. 2.Doric order uses a cushion-like capital, tapered shaft, and lack of base. 3.The Ionic order of column uses a curved volute capital, straight fluted shaft, and stepped base. 4.The Corinthian order uses acanthus leaf capital, straight fluted shaft, and a stepped base. 5.Composite, which is more ornamental than the Corinthian.

23. Romans improved the Greek idea of an amphitheater

24. The way an ellipse has two foci makes the sound travel better

25. The reflective properties of an ellipse make it interesting mathematically for acoustics & optics

26. The Colosseum supported up to 50,000 people, and admission was free. Each class or group had different sections to sit in the amphitheater and different entrances to use, reflected in the ticket needed for admission and the numbered archways to enter. Four arches were restricted to ordinary citizens and were used by the emperor and his family, the senators, vestal virgins, priest, and magistrates.

27. There were 80 entrances to the Colosseum. While the events at the Colosseum were free, each audience member needed to have a ticket to enter. The Romans developed the ticket system so people could locate their seats by knowing what section their seats were in and what entrance to go into. The privileged (emperors, vestal virgins, and senators) had the better seats while other citizens sat according to their rank in society. The seats highest up went to plebeians and women. The Colosseum was built solidly of marble and stone, allowing it to stand for almost 2,000 years. Contemplate what the Venerable Bede, English historian and Benedictine monk (672/3 – 735) said regarding the Colosseum: “While the Colosseum stands, Rome will stand; When the Colosseum falls, Rome will fall; When Rome falls, the world will fall. ”

28. Roman aqueducts, aqueducts in Rome The Roman aqueducts not only provided drinking water for the Romans but indoor sewer systems that carried water away from the city and also supplied the bath houses with ample water, where the inhabitants of ancient Rome spent so much of their leisure time.

30. Arch of Drusus(Aqua Antoniniana) is located 1/2 mile east of Caracalla’s baths.Caracalla’s baths

31. Nero’s Aqueduct(Arcus Neroniani), built by the emperor Nero(54-68 A.D.)

32. Porta Maggiore, aqueduct still standing over two important ancient roads, the Via Praenestina and the Via Labicana.

33. Rome's magnificent Trevi Fountain, built in the 1700s, still relies on sections of an ancient aqueduct for its water

35. Cutaway view of a typical Roman street during the Roman Empire, showing lead water pipes and a central channel for sewage under the pavement. Perpendicular connections brought sewage from nearby homes and

37. ROMAN BATHS

39. Using the scientific knowledge that heat rises in order to heat the baths.

40. Hypocaust Heating System was used to heat the houses as well as the baths.

42. The Roman Forum

43. Apartment housing was where the poorer people lived. They could not afford to buy, so they rented.

44. This is what it would have looked like.

45. Housing for the wealthier Romans, had many rooms.