#azimuthal equidistant

[map-projection-showdown]

KAVRAYSKIY VII vs AZIMUTHAL EQUIDISTANT

Kavrayskiy VII Pseudocylindrical Compromise

Created in 1939 by Vladimir V Kavrayskiy (Sometimes transcribed from Cyrillic differently, Kavraisky seems to be the most common alternative, used by G.Projector) for use as a general-purpose compromise projection in Soviet atlases. It has seen little use outside the area of the former Soviet Union, where usually the Robinson is used instead.

Mathematically it is the same as the Wagner VI projection horizontally compressed by sqrt(3)/2, however it has very low distortion values on many metrics, comparable to the Winkel Tripel.

This projection is mentioned in passing under the Winkel Tripel's entry in xkcd 977.

Azimuthal Equidistant Azimuthal Equidistant

While it may have been known as far back as the ancient Egyptians, the Azimuthal Equidistant projection was first described by al-Biruni around the year 1000. As an equidistant projection all distances from the chosen centre point can be measured correctly, meaning it is often used for things like missile range maps and other uses where only the distance from a single point is important.

Because of its circular shape, the polar aspect is often used for maps in logos such as the emblem of the UN. It can also be cropped to show a single hemisphere, and can be shown as two hemispheres side by side in the equatorial aspect like this.

[link to all polls]

Political:

Tissot's Indicatrices:

Images created by Tobias Jung (CC BY-SA 4.0) from map-projections.net

[patricia-taxxon]

it's clear why flat earthers chose the azimuthal equidistant projection for their map, cus its the one that lets commercial flights go all around the earth without teleporting by just going in a circle around the north pole. but like, why center it on the north pole? why is antarctica the one that gets stretched out into the barrier between terra & infinity? it's gotta be northern hemisphere bias, like if a majority of flat earthers lived in australia or south africa or southern argentina/chile then they'd pick the other pole to be the ice wall.

[o-craven-canto]

Highlights:

CYLINDRICAL (meridians are equally spaced vertical straight lines, parallels are horizontal straight lines)

Equirectangular (ca. 120 CE): my favorite! X-Y coordinates on the map correspond exactly to latitude and longitude on Earth's surface, simple and straightforward. Parallels and meridians are all evenly spaced perpendicular lines. Doesn't preserve perfectly shapes or relative sizes, but approximates both.

Cassini (1745): the equirectangular projection, if first Earth is rotated 90° so that the central meridian becomes the Equator

Mercator (1569): gets a bad rep because it inflates areas at high latitudes (so mostly northern continents, since the southern are close to the Equator). In fact, it cannot show the Poles because they'd be infinitely far away. However, it perfectly preserves shapes and it's useful for navigation because sailing with constant bearing always traces a straight line on this map. Some variant of it is used in most web maps.

Gall (1855): variant of Mercator's that can actually show the poles. Landmass shapes are no longer perfect.

Gall-Peters (1855): kinda the reverse of Mercator: they sacrifice landmass shapes to preserve perfectly their relative areas. Landmasses near the Poles are squashed rather than stretched infinitely. Lambert (1772) has a less extreme version.

PSEUDOCYLINDRICAL (the central meridian is a vertical straight line, but other meridians may be curves, though still equally spaced on any given parallel; parallels are still horizontal straight lines)

Ortelius (1540): preserves neither shapes nor areas, but compromises between both. All meridians except the central one are arcs of circles.

Mollweide (1855): preserves relative areas. Fits exactly in an ellipse, and all meridians except the central one are arcs of ellipses.

Collignon (1865): triangle. Preserves relative areas, somehow.

Goode Homolosine (1923): preserve relative areas and keep landmass shapes reasonably well, at the price of cutting huge gashes through the oceans.

Loximuthal (1935): constant bearing lines are straight lines on the map, like in Mercator. Preserves neither shapes nor areas. Weirdly asimmetrical hemispheres.

Robinson (1963): preserve neither shapes nor areas, but approximates both quite well. Kavraisky has evenly spaced parallels. The similar Equal Earth (2018) preserves relative areas.

CONIC (meridians are converging straight lines, parallels are arcs of circles)

Equidistant conic (ca. 150 CE): another of the old ones. Preserves only the distances along meridians, like the equirectangular.

PSEUDOCONIC (the central meridian is a straight line, the others may be curves)

Nicolosi globular (ca. 1000): splits the map in two circles, replicating the feeling of watching the world from space from two sides.

Werner (ca. 1500): heart-shaped, preserving relative areas, with the parallels being concentric circles around the North Pole.

AZIMUTHAL (meridians are straight lines meeting at the center, parallels are concentric full circles)

Gnomonic (ca. 580 BCE): probably the oldest map projection. Unfortunately it can only show at most part of one hemisphere, with the Equator being infinitely far away, much like the Poles in Mercator.

Stereographic (ca. 150 BCE): as before, but only the opposite pole is infinitely far away. The far hemisphere is still distorted, so it's still used in two parts, each centered on one pole.

Orthographic (ca. 150 BCE): basically just what the Earth would look like if observed from infinite distance: it shows exactly one hemisphere.

Azimuthal equidistant (ca. 1000): all parallels are full circles centered on the North Pole, and the South Pole is also a circle surrounding all. The map used on the flag of the United Nations. Most Flat Earthers think the Earth has this shape.

Two-point equidistant (1919): preserves distances on the straight line that passes thrrough two arbitrary points. A favorite of history atlases: it's usually used to portray Asia with as little distortion as possible despite its unfortunate proximity to both North Pole and Equator.

Hao projection or plane terrestrial globe (2002): popular in China, replicates as much as possible the curvature of a globe.

PSEUDOAZIMUTHAL (central meridian and equator are straight lines; other meridians curve toward the central meridian, other parallels curve away from the equator)

Wiechel (1879): the meridians form a pinwheel! Preserves relative areas, but which great distortion of the opposite hemisphere.

Aitoff (1889): looks like the Mollweide with diverging parallels. Mostly relevant because of:

Winkel Tripel (1921): arithmetic mean between Aitoff and equirectangular; the map used by National Geographic.

OTHER

Peirce quincuncial (1879): a perfect square that can be tiled regularly in all direction. I think Flat Earthers should start claiming that Earth look like this and that there are infinite copies in every direction.

Van der Grinten (1904): built ad hoc to map the Earth onto a circle, preserving exactly neither area nor shapes.

Craig's retroazimuthal or the Mecca Map (1909): looks crazy, but preserves the direction from any place on Earth to one specific point; in fact it was invented to help Muslims find easily the direction to the Mecca.

Cahill's Butterfly (1909): adorable, and can be folded into a perfect octahedron.

Dymaxion (1943): approximates shapes and areas, and preserves close connections between continents, at the price of a really weird shape.

[onecornerface]

Flat Earthers, Will Duffy, and the Final Experiment

Will Duffy has organized a trip to Antarctica for several flat-earthers and several round-earthers, to make observations together (especially of the overhead-circling 24-hour sun visible in the southern summer) and make progress in the "debate." The trip is happening in a few days. This has been the #1 topic for both flat-earthers and anti-flat-earthers making videos for the last year.

Throughout all this, it's been sad and remarkable watching Duffy's gradual loss of innocence. All the top flat-earthers have always said they wanted to go to Antarctica-- and all of them have always agreed that observing a 24-hour sun in Antarctica was impossible on a flat earth model, so such an observation would falsify flat earth theory. They acted confident that there was no 24-hour sun in Antarctica.

So, Duffy started this project in the hopes that flat-earthers would be open to the project and be excited to finally get their wish. A few flat-earthers agreed to go, but most rejected it vehemently.

Duffy has been pretty much the nicest guy ever in his treatment of flat-earthers. Over the last year, he has been disappointed again and again. Many flat-earthers have changed their story in sudden and drastic ways-- now saying that the observations in Antarctica don't matter at all, that the Gleason's Azimuth Equidistant Projection Map is no longer important (but haven't presented an alternative), that any flat-earther who accepts the free trip to Antarctica is a sell-out, and that Duffy and all the round-earthers going on the trip are literally possessed by demons.

[almostfancywombat]

1421

Note: Theoreticians have long postulated that Siberian migrants crossed the Bering Strait and founded modern-day America between the 30th and 10th millennium BC. Later traceable contacts, minor as they would be, are accredited to the Phoenicians and Portuguese, whose ships met demise and never returned to their homeland. However, the history of human migration and exploration is divisive and far more nuanced than it is presented in books, and in an era where oral myths and traditions were enough to revise history, time and space came together in a single tantalizing riddle when Gavin Menzies proposed that a Chinese sailor discovered the Americas in 1421. [y'all I hated this book so much I had to write an essay rant]

Ma Sanbao, descended from the Mongol empire and an area in modern Uzbekistan, is the Chinese explorer at the forefront of Menzies’ conspiracy. After conscription into the Chinese army in late childhood, nineteen-year-old Ma Sanbao distinguished himself as an officer and diplomat with imperial connections. Under the tutelage of the recently ascended Yongle Emperor, Ma Sanbao became Zheng He. With the country in disarray following wars, the Ming courts sought to display China’s power while returning foreign treasures.

Peculiarly, Menzies’ iteration deviates from traveling to South and Southeast Asia and depicts Zheng He visiting every corner of the globe, excluding the entire European continent. An index of supporting evidence includes thousands of: (1) archaeological artifacts such as pottery; (2) cartographical evidence from maps penned during the late Ming era; and (3) astronomy-related devices used for circumnavigating. (pp. 429-462)

In addition, Menzies claims Chinese seamen toured Maya lands, hunted in Greenland, and established trade ports in the Amazon. His travels to the supposed locations of Zheng He’s voyages support these claims. Accompanying unique personal experiences, vignettes told in a lively, engaging style propose an alternative and ultimately faulty reimagining of exploration history as modern historians know it. The chronology presented by Menzies falls under scrutiny when analyzing the Piri Reis map, one of his primary sources.

Named for a famed Ottoman admiral and cartographer, the Piri Reis map is incorrectly believed to be the most accurate cartographical catalog of the 16th century. Pertaining to Menzies' assertions, the closest the map veers towards depicting North America hardly represents the continent, save for a slim portion of coastline and an island labeled Antila, which may be modern-day Newfoundland.

This fascinating relic of navigators enters the scope of ice-age civilizations, shifting poles, and ancient astronauts, i.e., aliens. Charles Hapgood tailors the Piri Reis to justify a “pre-existing notion of an ice-free Antarctica.” He believed the earth’s poles had shifted, and the Piri Reis’ sources originated from maps of an ancient, unknown civilization that accurately mapped the coastline of a piece of South America. Hapgood also believes this part of the continent broke off to form Antarctica.

Swiss writer Erik von Daniken proposed the concept of “an azimuthal equidistant projection,” which, in brief, denotes extraterrestrials. Many would later disprove the Hapgood Hypothesis using Hapgood and Daniken’s evidence against their claims. Finally, Paul Lunde proposed that Piri Reis ran out of parchment and turned the coastline to the east to make space. It is no mystery why a theorist like Menzies would manipulate this map to his guiles; the phenomenon of Piri Reis lies solely in its earlier complement date, as more accurate cartography would arise in the same decade. An additional account from January 2009 presents another map assumedly dated to 1400 as “plainly a hoax.” Although the Shanghai bookshop that founded it claims the object as a late Ming-era artifact, the map depicts the Americas as enormous; yet each curve of Alaska and the Yucatan peninsula is accurately measured and mapped. Scholars, domestic and abroad alike, rubbish the find; the cartography depicted is stylistically European, while the characters are not in the proper medieval variation. A cursory study of this instance would lead one to believe in its ultimatum, but further research displays a bias among experts in the given field.

As Chinese dynasties tended to destroy evidence of prior ones, this replica would suffice in lieu of a verifiable original. The closest one could hope for a cartographic delineation of the Americas predating Columbus is the Vinland map, which shows a North American coast despite being of Greenland. After much scrutiny, Vinland scholar RA Skelton asserted it remains “the only known cartographical delineation of American lands [prior to the voyages] of Columbus and Cabot.” Comparatively, the Vinland map presents a historical origin in Viking Leif Eriksson, who claimed the first known settlement of modern America by outsiders. Considering the Shanghai map, faking a circumnavigation is simply baseless grounds for further chauvinism, which has entrapped outsiders with its perceived novelty. Menzies frequently misinterprets Chinese imperial policy and fails to cite sources, and those he does mention are fraudulent.

Furthermore, Menzies allots amateur studies excessive weight on his website, Friends of the 1421. Herein, Menzies cites a Croatian geneticist who reports on long-standing local rumors stating the presence of “Oblique-eyed yellow Easterns” in the Adriatic sometime before 1522. If a fleet of Chinese junkers had appeared in the Adriatic, in a continent of intellectuals undergoing a renaissance of history, bureaucracy, and art, such an instance would have survived the five-hundred-odd years since then, yet evidence to support this claim has not been found. Even outside the inaccurate and bloated Yellow Registers Archives of Imperial Ming China, the only evidence connecting Ming voyages with European affairs is a mythological figure resulting from misinterpreting sources.

With such verbose diction, 1421 is more analogous to a novel than a factual, historical account. The claims presented rival Velikovsky in terms of fallacies and reach; there is an apparent surplus in Chinese geographical history, yet leaves much for desire in a lack of support with socio-economic policies. The Ming Emperors, suspicious and vigilant against foreign presence, would guard such precious information for the Europeans, equating to high risk with little benefits for the Chinese.

While any discovery entails a comprehension of significance before facts, 1421 demonstrates a view with little space for refutation. This stringent speculation ultimately classifies Menzies’ work as pseudohistory; abusing scientific tools to rewrite world history on such a grand scale is impossible, and the endeavor is enterprising at best.

[tomatodeals]

Riley Inventive Options 1943 Flat Earth World Map | Polar Azimuthal Equidistant

Value: (as of – Particulars) Riley Inventive Options 1943 Flat Earth World Map | Polar Azimuthal Equidistant Projection Map | Massive Wall Artwork Poster Print (3 Sizes) (11"x16")GREAT POSTERS FOR THE OFFICE: Are you struggling so as to add that basic contact of magnificence to a room in your workplace? Classic type posters assist broaden your adorning choices and harness the ability of…

[very-gay-alkyrion]

Wouldn't this work if you constructed said """square""" on a cone, and then projected it onto a 2D surface using an azimuthal equidistant projection

I love seeing a meme and being like oh, tumblrs going to love this one

[map-projection-showdown]

AZIMUTHAL EQUIDISTANT vs STEROGRAPHIC

Azimuthal Equidistant Azimuthal Equidistant Round 1: [Azimuthal Equidistant vs Kavrayskiy VII]

Stereographic Azimuthal Conformal Round 1: [Stereographic vs Eckert IV]

Two azimuthal projections face off in this poll, who will win between these two projections that were both first used by the Ancient Egyptians for star charts.

While the images I'm using here show them in different aspects, both of them can be used differently, the stereographic projection is usually shown in two hemispheres as it can't show the whole world from one tangent point, while the azimuthal equidistant is usually shown in a single circle due to its equidistant property.

If you check out the direct comparison below you can see the difference when they both use the same equatorial hemispheres, the stereographic projection being conformal gives it more accurate shapes, but of course also leads to greater size distortion.

[Direct comparison on map-projections.net]

[link to all polls]

[moondeluge-a]

Johngalli’s interest expanded into star maps temporarily in addition to planetary interests. 

At that point in his life, he attempted to memorize the inner-workings of the the azimuthal equidistant projection. This would lead him to eventually get the three tattoos of the world on his back and shoulders. 

He would receive these not too long after his cataracts began to truly injure his sight to an irreversible extent.

[generasbir]

Peta bumi menjadi dua kubu besar antara Rusia dan Amerika saat perang melawan Nazi Jerman

Peta dunia menjadi dua kubu Besar, INI adalah peta perjuangan dunia yang akan menandai titik balik peradaban. Perjuangan membagi dunia menjadi dua kubu besar: mereka yang mendukung kita (dalam berbagai derajat) dan mereka yang melawan kita (juga dalam berbagai derajat). Di antara ekstrem-ekstrem ini ada yang netral, ada yang condong ke satu arah, ada yang lain. Semua gradasi ini dijelaskan dalam kunci di halaman yang berlawanan.

Beberapa poin penting mengenai peta ini harus diperhatikan. Yang pertama adalah bahwa seluruh konflik berputar di sekitar A.S. Ini bukan hanya karena penempatan A.S. di pusat penyebaran: melainkan terletak pada sifat perjuangan. AS adalah poros (a) karena posisi geografisnya, yang merupakan pusat lautan; selengkapnya klik dibawah 👇.

[rvexillology]

UN redesign

from /r/vexillology Top comment: Definitely prefer it to the weird azimuthal equidistant projection on the current one

[maptitude1]

An azimuthal equidistant projection centered on Argentina

[itomakitsunogi2023]

世界の政府は、世界は丸いと大衆に信じさせようとしています。

しかし、政府が世界の実際の構成について問題に対処する方法を知りたいとき、彼らは極座標方位平板地図を参照する。

実際、米軍は何百人もの兵士や民間人を使って、展開地域の正確な地図を作成しています。

その地図が公開されることはほとんどありません。

下の写真は、ホワイトハウスが公開し、インターネットに掲載されているホワイトハウス・��チュエーション・ルームの公式ビデオツアーの一コマで、ホワイトハウス・シチュエーション・ルームにある方位等角地図の極座標投影図です。

肝心なときに、アメリカ政府が知りたがっているのは、地球の本当の姿、つまり平らな地球なのです。

The governments of the world want the masses to believe that the world is round. However, when governments want to know how to address issues on the real configuration of the world, they reference a polar equidistant azimuthal flat earth map. Indeed, the U.S. Military employs hundreds of soldiers and civilians in producing accurate maps of areas of deployment. Those maps are almost never made public. Below is a frame from an official video tour of the White House Situation Room, published by the White House and posted on the internet, showing a polar projection of an azimuthal equidistant map in the White House Situation Room.When it really counts, the U.S. Government wants to know the real configuration of the earth: a flat earth.

『The-Greatest-Lie-on-Earth-Proof-That-Our-World-Is-Not-A-Moving-Globe』より引用

[greenteaforbreakfast]

azimuthal equidistant ftw :)

@drszoszie a legjobb erre mindig a földgömb lesz, ha otthon nincs, akkor gmapsen zoomolj ki és nézegesd úgy. A 3d nem basz át. A fenti kép amúgy nem rossz, csak nehéz tényleg csak a sötétkékeket látni, pláne ott, ahol sok van egymás mellett, azért tűnik úgy, mintha Európa nagyobb lenne a kelleténél. De ha Európa országainak sötétkékjét összegyúrod, akkor azt simán bele lehet teríteni a kontinentális usa egy szem sötétkékjébe.

Az a helyzet ugyanis, hogy az USA és főleg Oroszország tényleg mocskosul kurvanagyok az európai országokhoz, vagy akár egész Európához képest. Csak az elterjedt vetületek (nem csak a Mercator!) miatt, pláne európaiként, nem vagy hozzászokva. Mindenki olyan térképeket szeret ugyanis nézegetni (mutogatni és tanítani), amiken a saját országa nagy és jól kivehető. Az ausztrálok pl teljes nyugalomban vágják ketté Grönlandot, hogy a kontinensük a térkép közepére kerüljön. Ezért is érdemes néha földgömböt forgatni, elég sok minden kaphat új perspektívát általa.

Ha nem lenne a Mercator világtérkép, ahol Grönland és Kanada is indokolatlanul nagyra van torzítva, lehet, hogy most egy kicsivel kevésbé idióta felvetéseket kellene komolyan vennünk. All my homies hate the Mercator projection. :(

[harrelltut]

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[mapsburgh]

A flat earth proposal

Ancient flat earth theories envisioned the earth as essentially equivalent to a cylindrical projection of the real earth. This meant that E-W and N-S were both straight lines that remained at right angles to each other across the whole surface of the world. This is the simplest form of a flat earth model to construct. (map below by Cosmas Indicopleustes, one of the few medieval Westerners who actually believed in a flat earth)

Modern flat earth theories most commonly envision the earth as matching an azimuthal equidistant projection centered on the north pole. This turns E-W into circles rather than straight lines, and makes N-S lines converge at the north pole and radiate outward to the south.

Compared to the ancient model, this modern model has several features that maintain its plausibility for flat earth believers:

1. It avoids interrupting the earth’s surface anywhere that people commonly travel. A cylindrical projection requires an interruption -- most commonly along the center of the Pacific Ocean, though you can in theory put it anywhere. But people travel east to west across the Pacific (and any other possible interruption location) all the time. You’re going to have trouble convincing someone who flew westward from California to Australia that their plane actually looped around eastward through the Atlantic and Indian Oceans, as would be required on a flat earth of the ancient model.

2. It maintains the connectivity of places around the Arctic. There is increasing travel through the Arctic (I flew across it in both directions on a recent trip from DC to Beijing and back to Chicago), which creates the same plausibility challenges if you’re using a cylindrical projection that ends at the arctic.

3. It can handle the fact (easily verifiable through telecommunications contact with people around the world) that the sun is always in the sky somewhere. The ancient model posited that the sun moved from east to west in a line across the earth, then returned by traveling beneath the world -- during which time the entire earth would have night. The modern model allows the sun to move in a circle above the earth, illuminating different areas like a spotlight.

But the azimuthal equidistant flat earth model presents some problems of its own. While sizes and shapes of land masses close to the north pole are not too wildly distorted, things in the southern hemisphere are way out of proportion. A flat earther using this model is committed to the claim that Australia is actually much, much wider from east to west than conventional maps would claim -- something that you’d think Australians themselves would have noticed. (Some flat earth maps correct for this by putting all of the E-W stretching into the oceans so that the southern continents stay the shapes we expect. Because this is an ad hoc correction of just the land areas, these maps never include a graticule whose inconsistencies would give away the game.)

The azimuthal equidistant model also requires positing that Antarctica is positively enormous, stretching around the whole outside of the world. Flat earthers have tended to make good use of this idea, by describing Antarctica as an impassable ice wall that separates us either from the void, or from unknown outer lands. But it’s still an awkward bit of geography.

I want to propose an alternative flat earth model: an infinitely tiled Pierce quincuncial projection.

By bringing each corner back together in the south, this projection avoids the major southern hemisphere distortions of the azimuthal equidistant model. A single quincuncial earth would generate some issues of its own with the significant interruptions between the four lobes of the south, most notably breaking Antarctica into four pieces. But those problems can be solved by tiling this projection infinitely. If, for example, you travel to the part of Antarctica near South America and then begin to circumnavigate in an easterly direction, you would wind up in the southern Africa corner of the next world over. And since these different worlds are all precisely identical, your counterpart in another world would have just entered your original world’s Africa lobe, making it seem as if you had simply circumnavigated Antarctica on a round globe.

One seeming hitch to this model is what happens at the non-pole junctions. It seems as if on the tiled map you could set out due west from Ecuador and wind up in the adjacent world’s Ecuador, or likewise going south from India, etc. The thing to remember here is that when you cross the border between segments, your direction changes 180 degrees. Instead of going west from Ecuador in your original world, you’d suddenly be going east toward Ecuador in the next world. It’s the equivalent of getting unexpectedly turned around and heading back the way you came on the round earth. And since your counterpart from the adjacent world would be doing the same thing, there would be no apparent difference to anyone observing this, even yourself!

Because the quincuncial projection is a square, it also resolves the meaning of several Biblical references to the “four corners” of the earth, which have produced problems for biblical literalist flat earthers working with the clearly circular azimuthal equidistant model.

(Obligatory disclaimer: I’m a geography professor, so I obviously don’t actually believe the earth is flat, but I find examining the features of various flat earth models to be an entertaining intellectual exercise.)