Cosmic Distance Ladder on Instagram: "The Earth is round, but maps (or computer and phone screens) are flat. So, we have to apply a projection to map the round Earth onto a flat surface. Ideally, we would like this projection to have three desirable properties: • Area-preserving. The projection should not stretch one part of the Earth to look larger than another part that actually has the same surface area. • Shape-preserving.(Mathematicians call this the “angle-preserving” or “conformal” property.) The projection should not squish or stretch the shape of an object: a round landmass should not become elliptical, for instance. • Grid lines. Lines of latitude should be horizontal; and lines of longitude (also known as “meridians”) should be vertical. Unfortunately, these three properties form a trilemma: any given projection can have two of these three properties, but not all three at once. The Mercator projection is the most famous. It is shape-preserving and has grid lines, making it particularly suitable for navigation. But it distorts area like crazy, making Greenland for instance look almost three times larger than Australia by area, when in fact it is over three times smaller. The Gall-Peters projection removes the area distortion, and keeps the grid lines - but at the cost of totally messing up shapes. Africa is way too tall and skinny; Canada too short and wide. The Mollweide projection tries its best to preserve both area and shape, and gives up entirely on straight grid lines. The relationship between area and shape is in fact fundamentally different for spheres and for planes, so no projection can preserve both of them perfectly; but Mollweide comes the closest. Can’t choose? Why not try the Winkel Tripel projection, which compromises by being only slightly bad at preserving areas and shapes, or keeping the grid-lines straight. Everything in this projection is slightly imperfect, but it tries to balance its faults evenly. There are an infinite number of possible projections. What projection is your favorite? #DistanceLadder #geography #MapProjections #3DGeometry #topology #mathematics #WhyNobodyLikesMercatorProjections"

27 likes, 1 comments - cosmic_distance_ladder on February 21, 2026: "The Earth is round, but maps (or computer and phone screens) are flat. So, we have to apply a projection to map the round Earth onto a flat surface. Ideally, we would like this projection to have three desirable properties: • Area-preserving. The projection should not stretch one part of the Earth to look larger than another part that actually has the same surface area. • Shape-preserving.(Mathematicians call this the “angle-preserving” or “conformal” property.) The projection should not squish or stretch the shape of an object: a round landmass should not become elliptical, for instance. • Grid lines. Lines of latitude should be horizontal; and lines of longitude (also known as “meridians”) should be vertical. Unfortunately, these three properties form a trilemma: any given projection can have two of these three properties, but not all three at once. The Mercator projection is the most famous. It is shape-preserving and has grid lines, making it particularly suitable for navigation. But it distorts area like crazy, making Greenland for instance look almost three times larger than Australia by area, when in fact it is over three times smaller. The Gall-Peters projection removes the area distortion, and keeps the grid lines - but at the cost of totally messing up shapes. Africa is way too tall and skinny; Canada too short and wide. The Mollweide projection tries its best to preserve both area and shape, and gives up entirely on straight grid lines. The relationship between area and shape is in fact fundamentally different for spheres and for planes, so no projection can preserve both of them perfectly; but Mollweide comes the closest. Can’t choose? Why not try the Winkel Tripel projection, which compromises by being only slightly bad at preserving areas and shapes, or keeping the grid-lines straight. Everything in this projection is slightly imperfect, but it tries to balance its faults evenly. There are an infinite number of possible projections. What projection is your favorite? #DistanceLadder #geography #MapProjections #3DGeometry #topology #mathematics #WhyNobodyLikesMercatorProjections".

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