Game of chess anyone?
This is pretty cool. What we are seeing here is an area of 23 x 20 kilometres along the Idaho-Montana border crammed between Clearwater and Bitterroot National Forests. You will notice a checkerboard pattern within the land area; each square covering an area of around 1.6 x 1.6 kilometres. Each square hosts trees, which are harvested at different times and have different timber densities and regrowth stages. As a result, this natural pattern has formed.
The image was taken with the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on-board Terra, the flagship satellite of NASA’s Earth Observing System (EOS).
-Jean
Image courtesy of NASA
Can you flatten a sphere?
The answer is NO, you can not. This is why all map projections are innacurate and distorted, requiring some form of compromise between how accurate the angles, distances and areas in a globe are represented.
This is all due to Gauss’s Theorema Egregium, which dictates that you can only bend surfaces without distortion/stretching if you don’t change their Gaussian curvature.
The Gaussian curvature is an intrinsic and important property of a surface. Planes, cylinders and cones all have zero Gaussian curvature, and this is why you can make a tube or a party hat out of a flat piece of paper. A sphere has a positive Gaussian curvature, and a saddle shape has a negative one, so you cannot make those starting out with something flat.
If you like pizza then you are probably intimately familiar with this theorem. That universal trick of bending a pizza slice so it stiffens up is a direct result of the theorem, as the bend forces the other direction to stay flat as to maintain zero Gaussian curvature on the slice. Here’s a Numberphile video explaining it in more detail.
However, there are several ways to approximate a sphere as a collection of shapes you can flatten. For instance, you can project the surface of the sphere onto an icosahedron, a solid with 20 equal triangular faces, giving you what it is called the Dymaxion projection.

The Dymaxion map projection.
The problem with this technique is that you still have a sphere approximated by flat shapes, and not curved ones.
One of the earliest proofs of the surface area of the sphere (4πr2) came from the great Greek mathematician Archimedes. He realized that he could approximate the surface of the sphere arbitrarily close by stacks of truncated cones. The animation below shows this construction.

The great thing about cones is that not only they are curved surfaces, they also have zero curvature! This means we can flatten each of those conical strips onto a flat sheet of paper, which will then be a good approximation of a sphere.
So what does this flattened sphere approximated by conical strips look like? Check the image below.

But this is not the only way to distribute the strips. We could also align them by a corner, like this:

All of this is not exactly new, of course, but I never saw anyone assembling one of these. I wanted to try it out with paper, and that photo above is the result.
It’s really hard to put together and it doesn’t hold itself up too well, but it’s a nice little reminder that math works after all!
Here’s the PDF to print it out, if you want to try it yourself. Send me a picture if you do!
Check out this Overview, which shows a maze of pipes and other equipment at an oil refinery in Corpus Christi, Texas. Due to its position on the Port of Corpus Christi — the fifth largest U.S. port and deepest inshore port on the Gulf of Mexico — much of the city’s economy is driven by the oil and petrochemicals industry. An average of 400,000 barrels of crude oil per day were exported from this port during 2018.
Instagram: https://bit.ly/2TcNg9q
27°50'00.4"N, 97°31'29.1"W
Source imagery: Nearmap
Here’s another fan favorite from 2018! Philadelphia is the largest city in the Commonwealth of Pennsylvania and the sixth most populous city in the United States, with a population of more than 1.5 million. The city played a pivotal role during the American Revolution, when it provided a setting for the signing of the Declaration of Independence in 1776 and the U.S. Constitution in 1787.
Instagram: https://bit.ly/2AoLOtl
39°57'10.0"N, 75°09'49.0"W
Source imagery: Nearmap
Sarychev Peak is located on Matua Island in the Kuril Islands of Russia. When the volcano erupted on June 11, 2009, the expulsion of debris caused significant interruption to air traffic between east Asia and North America. The eruption was also so great that astronauts aboard the International Space Station were able to photograph the plumes of ash and smoke rising from its cone, as the force of its shock waves dispersed all clouds covering the area.
Instagram: https://bit.ly/2PVjsff
48°05'26.9"N 153°11'59.0"E
Source imagery: DigitalGlobe
Guadalajara is the capital of and largest city in the Mexican state of Jalisco, with upwards of 5 million people living in its metropolitan area. It is also the second most densely populated municipality in Mexico, behind Ciudad Nezahualcóyotl. Guadalajara is a Mexican cultural hub, considered by many to be the home of mariachi music.
Instagram: https://bit.ly/2Q2JJZm
20°40'36.0"N, 103°20'51.0"W
Source imagery: DigitalGlobe
Kuala Lumpur Int'l Airport (KUL), Sepang, Selangor, Malaysia
https://goo.gl/maps/hv8ZrCXV1aq
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http://bit.ly/1WCSb2p
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There are two main passenger airports used for Kuala Lumpur, KUL and SZB.
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KUL is the IATA airport code for both KLIA1 and KLIA2 located at Sepang, and SZB is the IATA airport code for Subang airport ( Sultan Abdul Aziz Shah Airport ) which once was the international airport until KLIA opened.
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KLIA1 / KLIA2 is 40-60mins / 50 km south from Kuala Lumpur
Subang is 30mins / 26km west of Kuala Lumpur.
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KLIA / KLIA2 at Sepang is 55 km from SZB at Subang
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SZB at Subang = Sultan Abdul Aziz Shah Airport aka Subang [International] Airport. This was once the international airport from 1965 to 1998 when it had 3 terminals, only T3 is now used. It is the home of FireFlyz and Berjaya Air, flying mainly domestic Malaysian routes and short routes into neighbouring Thailand or Indonesia . Now that it is a regional airport Subang does not have 24 /7 facilities, so shops, eateries and taxis may be very limited at none peak times.
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KUL at Sepang = KLIA1 and KLIA2 terminals, it is only 1 airport and has been the main international airport since 1998 and is the home of Malaysia airlines and Air Asia. The majority of tourists and travellers will use the 2 terminals at this airport.
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KUL is the IATA code for Kuala Lumpur and shared by both KLIA1 and KLIA2 which ARE the same airport!
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OMG!
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Ref: http://bit.ly/1x6xSeM.
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#earthimages #earthimage #upintheair #abovetheclouds #satelliteimage #satelliteimages #EarthOverhead #overview #overvieweffect #kualalumpur #kualalumpurairport #KUL #KLIA1 #KLIA2 #airport http://bit.ly/2EB5HAo
Arizona Boneyard, Tucson, Arizona, USA
https://goo.gl/maps/jmL8Rvk5pbU2
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http://bit.ly/1WCSb2p
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Jetliners eventually reach end-of-life due to airframe wear, obsolescence, or economic conditions. Some jetliners are temporarily taken off flying status, and stored in a environment conducive to preservation. Others are kept for spare parts for flying aircraft.
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To protect airliners during their storage from wind and sun damage, engines and windows are tightly covered with white, reflective materials. A sealed airliner can thus be stored safely, for years, until the time comes to return it to active duty, or salvage. Eventually, all airliners are removed permanently from service and must be scrapped.
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Airliner “boneyards” in the deserts of the State of Arizona serve several functions: temporary storage, maintenance, parts reclamation, and scrapping. Four major airplane boneyards are located in Arizona, as shown in the map below.
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Today’s image is of a boneyard to the west of Tucson, Arizona.
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Ref: http://bit.ly/2q7G2Zn
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#earthimages #earthimage #upintheair #abovetheclouds #satelliteimage #satelliteimages #EarthOverhead #overview #overvieweffect #boneyard #arizona #arizonaboneyard #tucson http://bit.ly/2AdC19q
Putorana Plateau, Putoransky State Nature Reserve, Siberiahttps://goo.gl/maps/76K1Envfuxm
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https://ift.tt/2vlYbnW
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The area pictured shows part of the Putoransky State Nature Reserve, which is listed as a UNESCO World Heritage Site. Situated about 100 km north of the Arctic Circle, the site serves as a major reindeer migration route – an increasingly rare natural phenomenon – and is one of the very few centres of plant species richness in the Arctic.
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Virtually untouched by human influence, this isolated mountain range includes pristine forests and cold-water lake and river systems. The lakes are characterised by elongated, fjord-like shapes, such as Lake Ayan in the upper-central part of the image.
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Zooming in on the lake we can see that it is mostly ice-covered, with small patches of water peeking through around its lower reaches.
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Another feature of this area are the flat-topped mountains, formed by a geological process called ‘plume volcanism’: a large body of magma seeped through Earth’s surface and formed a blanket of basalt kilometres thick. Over time, cracks in the rock filled with water and eroded into the rivers and lakes we see today.
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This image, also featured on the Earth from Space video programme, was captured on 2 March 2016 by the Copernicus Sentinel-2A satellite.
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Text & Image: http://www.esa.int/
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#earthimages #earthimage #upintheair #abovetheclouds #satelliteimage #satelliteimages #EarthOverhead #overview #overvieweffect #siberia #PutoranaPlateau #Putorana #Plateau #unesco #space #sentinal-2a #copernicus #arctic https://ift.tt/2QL0zkI
Agricultural fields line the shores of the Itaipu Reservoir — a body of water that forms the border between Brazil and Paraguay. The area’s tropical climate makes it an ideal place to grow sugarcane, coffee, tea, and cotton.
Instagram: https://bit.ly/2Cfqo3q
25°18'20.3"S, 54°25'12.6"W
Source imagery: DigitalGlobe
The Judge Harry Pregerson Interchange is a 130-foot-tall (40 m) stack interchange near the Athens and Watts communities of Los Angeles, California. It is formed by the intersection of Interstate 105 (Glenn M. Anderson Freeway) and Interstate 110 (Harbor Freeway). For a full weekend in 2015, one of the interchange ramps was closed for filming the opening musical number of “La La Land.”
Instagram: https://bit.ly/2J9wQce
33°55'44.1"N, 118°16'50.1"W
Source imagery: Nearmap
In this Overview, thousands of cattle can be seen on a feedlot in LaSalle, Colorado – a small town roughly 50 miles (80 km) north of Denver. This particular feedlot has a capacity for 69,000 cows and is one of several owned by the largest cattle feeding company in the world. Other feedlots owned by company, located in Arizona, Idaho, Kansas, Oklahoma and Texas, have an estimated total feeding capacity of more than 900,000 head of cattle.
Instagram: https://bit.ly/2QmMYz1
40°19'31.5"N, 104°46'43.1"W
Source imagery: Nearmap














