In mathematics, the Roman surface or Steiner surface is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. This mapping is not an immersion of the projective plane; however, the figure resulting from removing six singular points is one. Its name arises because it was discovered by Jakob Steiner when he was in Rome in 1844. The simplest construction is as the image of a sphere centered at the origin under the map This gives an implicit formula of Also, taking a parametrization of the sphere in terms of longitude (θ) and latitude (φ), gives parametric equations for the Roman surface as follows: The origin is a triple point, and each of the xy-, yz-, and xz-planes are tangential to the surface there. The other places of self-intersection are double points, defining segments along each coordinate axis which terminate in six pinch points. The entire surface has tetrahedral symmetry. It is a particular type (called type 1) of Steiner surface, that is, a 3-dimensional linear projection of the Veronese surface. (Wikipedia).
Astronomy - Ch. 10: Mercury (4 of 42) Terrain and Color
Visit http://ilectureonline.com for more math and science lectures! In this video I will discuss the surface of the planet Mercury. The surface of Mercury is gray with crater everywhere. It pretty much looks like our Moon. I will also explain what are dorsa (wrinkled ridges), rupes (escar
From playlist ASTRONOMY 10 MERCURY
Astronomy - Ch. 10: Mercury (5 of 42) Significant Features
Visit http://ilectureonline.com for more math and science lectures! In this video I will discuss the significant features on Mercury. Yes there are “significant features” on Mercury. Even though the surface of may look gray, mundane, and covered with a “sea” of craters. But upon careful e
From playlist ASTRONOMY 10 MERCURY
Earth's sister planet has a symbol derived from a hand mirror. More physics and astronomy at http://www.sixtysymbols.com/
From playlist The Sixty Symbols Solar System
Teach Astronomy - Landscape of Mars
http://www.teachastronomy.com/ Mars has richly varied surface features. There are rocky planes, gullies, riverbeds, smooth sea bed floors, sand dunes. There are dust storms that encompass large fractions of the planet's surface during certain seasons. There are huge gullies and crevasse
From playlist 09. Outer Planets and Planetary Atmospheres
Teach Astronomy - Surface Ages
http://www.teachastronomy.com/ The longer a surface exists in the solar system, the more often it has been hit by interplanetary debris. Thus, when we compare different worlds or different parts of the same world, we can decide whether the surfaces are ancient or young based on the number
From playlist 09. Outer Planets and Planetary Atmospheres
Astronomy - Ch. 12: Mars (12 of 25) Major Surface Features of Mars
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will study some major surface features of Mars: Olympus Mons, Taris Bulge, Elysium Mons, Valle Marineris, 3 Large Shield Volcanoes
From playlist VIEWER REQUEST VIDEOS: PHYSICS MECHANICS
Astronomy - Ch. 11: Venus (6 of 61) Geographical Features (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain (Part 1) the types of volcanoes on Venus, shield volcanoes. I will discuss some of volcanoes on Venus: Terra, Mons, Regio, Wallis, Rupes, Tholus, Planum, Plaintia, and Paterra. Next video in
From playlist ASTRONOMY 11 VENUS
Surface of the Sun as You've Never Seen it
Our sun is an incredible fusion engine. From the surface of earth, we see it as a mere ball of light, but through amazing high-res imaging capabilities, we can observe real solar activities thanks to NASA's Solar Dynamics Observatory.
From playlist The Solar System
19. Baroque Extravaganzas: Rock Tombs, Fountains, and Sanctuaries in Jordan, Lebanon, and Libya
Roman Architecture (HSAR 252) Professor Kleiner features the baroque phenomenon in Roman architecture, in which the traditional vocabulary of architecture, consisting of columns and other conventional architectural elements, is manipulated to enliven building façades and inject them wit
From playlist Roman Architecture with Diana E. E. Kleiner
Materialism Podcast Ep 11. The Ultimate Construction Material
A great empire demands an equally great building material. In this episode, we cover the development and implementation of concrete throughout human history. We are joined by Marie Jackson, a research associate professor of geology and geophysics at the University of Utah, and an expert on
From playlist Materialism Podcast
Apollo 12 on the Ocean of Storms
Ultra high-resolution photos of this historic second manned mission to the moon, including breathtaking photos of the lunar surface. Credit NASA.
From playlist Earth And Its Moon
A brief history of representing the body in Western painting
Speakers: Dr. Steven Zucker and Dr. Beth Harris. Created by Beth Harris and Steven Zucker.
From playlist Art history basics | Art History | Khan Academy
Battle of the Romans and Barbarians (Ludovisi Battle Sarcophagus), c. 250-260 C.E. (Museo Nazionale Romano-Palazzo Altemps, Rome) Speakers: Dr. Steven Zucker and Dr. Beth Harris. Created by Beth Harris and Steven Zucker.
From playlist Art of the ancient Mediterranean | Art History | Khan Academy
Mars Express, the first planetary mission of the European Space Agency, was sent to the Red Planet in 2003. It sent a lander down to the surface, and although it failed to fully deploy , the orbiter has been taking pictures and mapping the surface ever since. It has produced high-resolutio
From playlist The Solar System