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This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles. As a result, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa. There is some controversy over the origins of the Mercator. The projection found on these maps, dating to , was stated by Snyder [1] in to be the same projection as Mercator's.
However, given the geometry of a sundial, these maps may well have been based on the similar central cylindrical projection , a limiting case of the gnomonic projection , which is the basis for a sundial. Snyder amends his assessment to "a similar projection" in Joseph Needham , a historian of China, wrote that the Chinese developed the Mercator projection hundreds of years before Mercator did, using it in star charts during the Song Dynasty.
The projection in use was the equirectangular projection. Portuguese mathematician and cosmographer Pedro Nunes first described the mathematical principle of the loxodrome and its use in marine navigation.
In , he proposed constructing a nautical atlas composed of several large-scale sheets in the cylindrical equidistant projection as a way to minimize distortion of directions. If these sheets were brought to the same scale and assembled, they would approximate the Mercator projection. In , Gerhard Kremer, known by his trade name Gerardus Mercator, announced a new projection by publishing a large planispheric map measuring by cm 80 by 49 in and printed in eighteen separate sheets.
This title, along with an elaborate explanation for using the projection that appears as a section of text on the map, shows that Mercator understood exactly what he had achieved and that he intended the projection to aid navigation.
Mercator never explained the method of construction or how he arrived at it. Various hypotheses have been tendered over the years, but in any case Mercator's friendship with Pedro Nunes and his access to the loxodromic tables Nunes created likely aided his efforts. English mathematician Edward Wright published the first accurate tables for constructing the projection in and, in more detail, in , calling his treatise "Certaine Errors in Navigation".
The first mathematical formulation was publicized around by a mathematician named Henry Bond c. However, the mathematics involved were developed but never published by mathematician Thomas Harriot starting around The development of the Mercator projection represented a major breakthrough in the nautical cartography of the 16th century.
However, it was much ahead of its time, since the old navigational and surveying techniques were not compatible with its use in navigation. Two main problems prevented its immediate application: the impossibility of determining the longitude at sea with adequate accuracy and the fact that magnetic directions, instead of geographical directions , were used in navigation. Only in the middle of the 18th century, after the marine chronometer was invented and the spatial distribution of magnetic declination was known, could the Mercator projection be fully adopted by navigators.
Despite those position-finding limitations, the Mercator projection can be found in many world maps in the centuries following Mercator's first publication. However, it did not begin to dominate world maps until the 19th century, when the problem of position determination had been largely solved. Once the Mercator became the usual projection for commercial and educational maps, it came under persistent criticism from cartographers for its unbalanced representation of landmasses and its inability to usefully show the polar regions.
The criticisms leveled against inappropriate use of the Mercator projection resulted in a flurry of new inventions in the late 19th and early 20th century, often directly touted as alternatives to the Mercator.
Due to these pressures, publishers gradually reduced their use of the projection over the course of the 20th century. However, the advent of Web mapping gave the projection an abrupt resurgence in the form of the Web Mercator projection. Today, the Mercator can be found in marine charts, occasional world maps, and Web mapping services, but commercial atlases have largely abandoned it, and wall maps of the world can be found in many alternative projections.
Google Maps , which relied on it since , still uses it for local-area maps but dropped the projection from desktop platforms in for maps that are zoomed out of local areas. Many other online mapping services still exclusively use the Web Mercator. As in all cylindrical projections , parallels and meridians on the Mercator are straight and perpendicular to each other.
In accomplishing this, the unavoidable east—west stretching of the map, which increases as distance away from the equator increases, is accompanied in the Mercator projection by a corresponding north—south stretching, so that at every point location the east—west scale is the same as the north—south scale, making it a conformal map projection. Conformal projections preserve angles around all locations.
Because the linear scale of a Mercator map increases with latitude, it distorts the size of geographical objects far from the equator and conveys a distorted perception of the overall geometry of the planet. A Mercator map can therefore never fully show the polar areas as long as the projection is based on a cylinder centered on the Earth's rotation axis; see the transverse Mercator projection for another application.
The Mercator projection maps all lines with constant bearing rhumbs mathematically known as loxodromes—those making constant angles with the meridians to straight lines.
The two properties, conformality and straight rhumb lines, make this projection uniquely suited to marine navigation : courses and bearings are measured using wind roses or protractors, and the corresponding directions are easily transferred from point to point, on the map, with the help of a parallel ruler for example.
As on all map projections , shapes or sizes are distortions of the true layout of the Earth's surface. The Mercator projection exaggerates areas far from the equator. Because of great land area distortions, some [ who? Mercator himself used the equal-area sinusoidal projection to show relative areas.
However, despite such distortions, the Mercator projection was, especially in the late 19th and early 20th centuries, perhaps the most common projection used in world maps, despite being much criticized for this use. Because of its very common usage, the Mercator projection has been supposed to have influenced people's view of the world, [9] and because it shows countries near the Equator as too small when compared to those of Europe and North America, it has been supposed to cause people to consider those countries as less important.
The Mercator projection is, however, still commonly used for areas near the equator where distortion is minimal. It is also frequently found in maps of time zones. Arno Peters stirred controversy beginning in when he proposed what is now usually called the Gall—Peters projection to remedy the problems of the Mercator, claiming it to be his own original work without referencing prior work by cartographers such as Gall's work from The projection he promoted is a specific parameterization of the cylindrical equal-area projection.
In response, a resolution by seven North American geographical groups disparaged using cylindrical projections for general-purpose world maps, which would include both the Mercator and the Gall—Peters. Practically every marine chart in print is based on the Mercator projection due to its uniquely favorable properties for navigation.
It is also commonly used by street map services hosted on the Internet, due to its uniquely favorable properties for local-area maps computed on demand. The Mercator projection was designed for use in marine navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome is preferred in marine navigation because ships can sail in a constant compass direction, reducing the difficult, error-prone course corrections that otherwise would be needed frequently when sailing a different course.
For distances small compared to the radius of the Earth, the difference between the rhumb and the technically shortest course, a great circle segment, is negligible, and even for longer distances, the simplicity of the constant bearing makes it attractive. So anything relevant you can share, we'd really appreciate. Github Desktop 2. Windows 10 home Disabling 2fa didn't help either.
I brought my VScode settings over via Github, that worked fine. Everything with deep linking is fine? Windows 7. I also reset my keychain access too! Installed GitHub Desktop 2. Chrome is Get the same issue. Same issue, GitHub desktop 2. Hasn't worked in Chrome, Firefox, Brave, or Edge. I figured out a way to login though, in the VM I added the existing repository already downloaded via the GitHub desktop for mac , and was then asked for credentials in order to be able to access the repository.
Logging in then happens in the GitHub desktop application and works fine. Thanks to everyone who has shared details about this. I have a couple of other questions that would be helpful for us as we continue to work to narrow down what could be causing this.
It'd be great if everyone could verify whether or not they have tried changing the default system browser and are still able to reproduce this error. If changing the default browser does not resolve things then we can deduce that it's a broader system issue preventing authentication from completing.
These are both things that we've seen cause various problems over the years. If you are running GitHub Desktop in a virtual machine that would also be helpful to know. I noticed this issue trying to log into Github Desktop with an Enterprise account after download. I clicked on Github. Same issue here in Bootcamp on a Mac. Windows 10 Pro Experiencing it in Firefox Mac client is working fine, but no joy with Windows. I was also running into this issue when running in a VM on Parallels.
For me, here were the reproduction steps:. I wasn't able to get around this through any browsers or re-installations, but I was able to find a workaround. Here's what worked for me. No changes to registry are needed, but still. I am having a similar issue, when I click "sign in with browser" my browser never opens. When Firefox is the default browser a pop up opens asking to run Firefox as admin, I click "OK" then Firefox never opens.
I changed the default browser to Chrome, clicking "sign in with browser" did nothing at first, 10 minutes later Chrome did open and I was able to login in the browser. After the initial 10 minute wait clicking sign in again immediately opens the Chrome browser. Maybe Firefox was working I just didn't wait long enough? I then discovered I was logged into the wrong account, I went back to github desktop and signed out, clicked sign in again, it took me back to a browser page "redirecting me to the application" and never gave me an option to enter my credentials.
In order to switch accounts now I need to go to Github in the browser, sign out there, then go and try to sign in from github desktop, this extra step is annoying Running Windows 7 64bit, Github desktop Version 2. Proposed solution - Revert Github to allow users to login directly from Github desktop and enter credentials there.
I'm having this issue too. The standard flow for logging into the application fails at the same spot, when redirecting back to the from the browser. The work around posted above works for me, however. System specs: Client: Fresh install of Github Desktop 2. I had a similar issue. After trying everything mentioned here unless I miss something similar I figured out a workaround due to GitHub Desktop currently supporting multiple protocols:.
If your browser does not redirect you back, please click here to continue. Thank you! I was using Microsoft edge to try and clone repository but it kept loading, nothing was happening I changed to chrome and boom, everything worked well. Tried various workarounds here, launching in administrator mode was the one that worked for me.
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