Tilting by a little more or a little less than 90 degrees maps the horizon to a very large circle-it appears to be nearly a straight line when projected stereographically. The sky lies on one side and the ground on the other, much like we see in “ordinary” photographs. FLEXIFY MOVIES FULLīut in such a projection we enjoy nearly a full 360-degree field of view along the horizon (impossible in an ordinary photo!), and this implies that there must be some serious distortion. See figure 3 for an example.Īnd if we tilt the viewable sphere a full 180 degrees, so that it is entirely upside down before projecting, then the horizon maps to the same circle as in the original projection. But now it is a circle with the sky on the inside-resulting in a fantasticallooking tunnel world. While stereographic projection has been used in cartography for centuries, in the 19th century Bernhard Riemann used it to gain a critical insight into the complex numbers. If one associates the projection plane beneath the viewable sphere with the complex plane-so that the sphere has radius one and rests precisely on the origin-then stereographic projection provides a one-to-one correspondence between the complex numbers and the points on the sphere except for the North Pole. Said another way: if a single point were added to the set of complex numbers, this “extended complex plane” could be placed in perfect one-to-one correspondence with the points on a sphere via stereographic projection. The extra point is called the point at infinity, and the sphere in this context is known as the Riemann sphere. It so happens that the field of complex analysis, from Riemann’s time to the present, has produced a cornucopia of conformal mappings from the extended complex plane to itself. This gives the panoramic photographer a deep reservoir of possibilities for producing flat images from the viewable sphere. Macs can get viruses, but do Macs need antivirus software?ĭo Macs get viruses? Do Macs need antivirus software? The answer isn’t as simple as it may seem. In this article, we look at the dangers faced by Mac users and the pros and cons of using Mac antivirus software. Historically, the Mac has been considered to be safe and secure for a number of reasons that we will go into below, but in recent years that has shifted considerably. In its report on the State of Malware in 2019 here, Malwarebytes said it saw a: “Significant rise in the overall prevalence of Mac threats, with an increase of over 400 percent from 2018”. The good news is that in its State of Malware report in 2020 Malwarebytes found that the amount of malware detected on macOS actually decreased by 38 percent. But before you breathe a sign of relief, Malwarebytes stated that the worst kind of malware, namely “backdoors, data stealers, and cryptocurrency stealers/miners, increased by more than 61 percent” in 2020.Īs for 2021, Malwarebytes indicated that “Overall Mac detections decreased by 38%, though Mac detections for businesses increased 31%”. It’s not only Malwarebytes that is reporting that viruses on the Mac is something to be concerned about: Apple is too! In May 2021 Apple’s software chief Craig Federighi took the stand at the Apple vs Epic trial and said that: “Today, we have a level of malware on the Mac that we don’t find acceptable.” Malware might be falling, at least for consumers, but other kinds of annoying programs continue to increase: “Malware accounted for just 1.5% of all Mac detections in 2020–the rest can be attributed to Potentially Unwanted Programs (PUPs) and Adware,” said Malwarebytes of 2021.
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