Recently added

What's new

Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject the collection had not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

5 September 2026

13 essays on the impossibility, the families, what is taught wrongly, what each projection optimises, what the numbers refer to, what a machine does with it and measuring distortion

The impossibility

What a cut buys

Six rungs count cuts and none measures one. A cut is a curve on the sphere with a length in kilometres, the shape distortion it removes is a falling function of that length, and the interruption everybody prints spends a hundred thousand kilometres to reach a figure the even-lobed curve reaches with sixty.

6 figures

Bigger triangles, and how much bigger depends on what is fixed. How well a survey can resolve Gaussian curvature, against the side of its triangles, under three things being held fixed. One triangle: the accuracy improves as the inverse SQUARE of the side, fitted exponent -2.000. A chain of fixed length, which is what every great arc was: bigger triangles mean fewer of them, and the exponent is -1.503 — exactly three halves. A network covering a fixed area: -0.999, exactly one. The trade depends on what a survey is short of.

The impossibility

How many triangles it takes

Rung eleven priced one triangle and recorded that a survey observes hundreds. Averaging n of them divides the noise by √n, and n is not free: a chain of fixed length holds fewer big triangles than small ones, so the accuracy improves as the side to the power three halves rather than two. Struve's 141 triangles of forty kilometres are worth exactly Gauss's seven of eighty-five.

6 figures

The families

Four radii of the Earth

Ten rungs handle the ellipsoid with an auxiliary latitude. Every one of those constructions also needs a radius, and the radius that makes each property exact is a different number: the published 6371 km is right for an area to half a part per million and wrong for a meridian distance by 559 — while the radius a conformal map needs is not a constant at all, and spans 6,739.

6 figures

One quantity, one region, and the exponent left free. The scale departure of six projections over the world, aggregated as a p-norm, against p on a logarithmic axis. At p = 1 the best is Eckert IV; at p = 64 it is Winkel tripel. Nothing about the maps changed between the two ends of the axis — only how much of the region a bad point is allowed to spoil. Drawn in no projection: the axes are an exponent and a score.

What is taught wrongly

The average was a choice of norm

Ten projections, one region, one measured quantity, and the only free decision left is how to turn a field into a number. Over the world's scale departure the ordering at the mean and the ordering at the worst case have a rank correlation of −0.04, all ten maps change position, and the exponent that produced each answer is stated nowhere.

6 figures

Two regions, three answers. Britain and New Zealand, 166° apart, with the pole of the best oblique conic under each of three objectives. Pooling the samples and taking an area-weighted score puts the pole in one place; refusing to let either region be worse than the other puts it somewhere else. The regions are drawn on Mollweide so that equal ground areas are equal page areas.

What each projection optimises

The pooled score abandons a region

Fifteen rungs optimise for one region. An atlas is several, and pooling their samples into one area-weighted score is what everybody does — which on Britain and New Zealand serves Britain 1.2 times worse than it could be served alone and New Zealand 125 times worse. The worst-case objective makes them equal at 33 and 59, and the cost of sharing rises with separation from 1.4 to 59.

6 figures

A surface whose curvature changes sign, and integrates to nothing. a wide ring of major radius 3 and minor radius 1, shaded by its Gaussian curvature. The outer half is positively curved like a sphere, at up to 0.250; the inner half is saddle-shaped and negative, down to -0.500; and the two circles between them, drawn as lines, are exactly flat. The integral of the curvature over the whole surface is zero, which is 2π times the Euler characteristic — and every impossibility in this collection rests on that number being 2 rather than 0.

What the numbers refer to

On a body with a hole, north can be up everywhere

Twelve rungs vary the body's shape and none varies its topology, which is what every impossibility here actually rests on. A torus has a nowhere-zero tangent field, a total curvature of zero rather than 4π, and a conformal world map with no cut and no singular point — and it still cannot be flattened, for the one reason that survives.

6 figures

Millimetres of horizontal move per kilometre of assumed height. How far the transformed latitude and longitude move when the height fed into a datum transformation changes by one kilometre, for four published transformations at five places. It runs from 7.7 to 121 millimetres per kilometre. A latitude and a longitude do not carry a height, so a two-dimensional coordinate cannot be transformed until somebody supplies one that is not in it.

What the numbers refer to

The height a coordinate does not carry

Ten rungs treat a datum shift as a map from one pair of angles to another. It is not one: the transformation runs through Cartesian coordinates, so the answer depends on the height — by 7.7 to 121 millimetres per kilometre depending on the datum and the place, which puts Lhasa 432 millimetres from where a height of zero would have said.

6 figures

The same tiling, turned. The cube's eight vertices, ringed, and eight cities, with the aspect of the cell each city falls in written beside it. The two panels are the same tiling: the same cells, the same areas, the same shapes, in the same numbers. Only where they sit has changed, and the eight cities get cells whose areas spread by 1.26 in one and 1.39 in the other. Drawn on Mollweide, in which equal ground areas are equal page areas.

What a machine does with it

The orientation is a policy

A polyhedral cell system has three free angles nobody scores. They cannot improve it: rotating the solid rotates every cell rigidly, so the distribution of cell areas is identical for every orientation there is. What they decide is who stands on the bad cells — and the eight cities measured here get a spread of cell area of 1.00 under the best turn and 1.50 under the worst.

6 figures

Measuring distortion

The sample was drawn on the page

Every mean in this collection integrates over the sphere, because that is where the ground is. A raster, a pixel loop and any figure that walks its own canvas integrate over the page instead, and the difference is exactly the covariance between the quantity being measured and the map's own area distortion — 7.2° of mean angular deformation on Miller becoming 18.0°.

6 figures

What a reprojection does, drawn where it does it. The angular deformation of the map that takes Sinusoidal's page to Gall–Peters's — which is what a reprojection is — shaded over the sphere and drawn on Mollweide so that equal ground areas are equal page areas. Both parents are equal-area, so the composite preserves area exactly; its mean angular deformation is 55.5° against 38.9° and 32.2° for the two maps separately. Composing two maps did not average their shape errors; it made a larger one.

Measuring distortion

Two indicatrices do not make a third

Reprojecting is composing, and the composite's indicatrix is not a function of its parents'. Mollweide followed by Hammer is gentler than either map over eighty per cent of the sphere; the sinusoidal followed by Gall–Peters is worse than both everywhere. What separates them is one angle, and it is the number rung ten showed the ellipse does not carry.

6 figures

Six regions, before and after. Six circular regions of unequal size on the equal-area rectangle, and the same six after the cartogram of four cities has been solved. Each drawn area is exactly its base area times the density it was asked for. The four that grow stay recognisably round; the two that shrink are drawn out into shapes that no longer resemble what they were, and nothing in the construction chose to treat them differently.

Measuring distortion

A cartogram keeps the shapes it inflates

Seven rungs build cartograms and none reads one back. Reading means recognising a region and dividing its drawn area by its base area, and the construction is against the reader twice: the correlation between how much a region grows and how much of its shape it keeps is −0.996, and the base area a reader has to divide by is the map the cartogram replaced.

6 figures

One current, two maps, and only one of them conserves it. A flow that has no sources or sinks anywhere on the sphere — it is the perpendicular of a stream function's gradient, so its divergence is zero by construction — drawn on two projections. The arrows on the right are the images of the same ground velocities as the ones on the left. On the equal-area map the drawn field is still divergence-free; on the other it is not, and the arrows drawn in the warning colour are where a reader measuring the picture would find a source or a sink that is not there.

Measuring distortion

A current drawn on a page has sources

Seven rungs project a scalar field and ask what the page does to its gradient. A wind or a current is the other half of what gets mapped, and the operator that matters for it is the divergence — which is preserved by an equal-area map exactly, by no other map at all, and by a conformal map least of anybody's expectation.

6 figures

Two places, one written coordinate. The lattice a coordinate written to 5 decimal places lives on, at 45° of latitude, where a cell is 1.11 metres north to south. Two real places a fifth of a cell apart are drawn as open marks and the single value they both round to as a filled one. The distance between them, computed from what was written, is exactly zero — an error a noise model cannot produce, since independent noise never puts two different points in the same place.

Measuring distortion

Rounding is not noise

Eight rungs treat a coordinate's error as noise that averages down. A published coordinate has a second error that does not: it is deterministic, it is shared between every point in the same cell, and at five centimetres apart ninety-three per cent of pairs come out as the same place — which no amount of independent noise can produce.

6 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

1 September 2026

20 essays on the impossibility, paths and directions, grids, and what a survey does, the families, what is taught wrongly, what each projection optimises, what a machine does with it and measuring distortion

How big a triangle it takes — the impossibility
The most compact shape depends on the paper — paths and directions
The score is not stable at any scale — paths and directions
Two charts are enough, and one is not — the impossibility
One pair of numbers, a hundred and twenty places — grids, and what a survey does
The exact map says the seam is smooth — the families
The ranking is not an order — what is taught wrongly
The answer is a set — what is taught wrongly
The first break is mostly its denominator — what each projection optimises
The nodes were evenly spaced — what each projection optimises
A tolerance in map units is not a tolerance — what a machine does with it
The worst point is not on the grid — measuring distortion
A mean that does not exist can still be printed — measuring distortion
There is no equal-area lattice on a sphere — measuring distortion
A refinement that stops moving — measuring distortion
Which of these numbers are the sampler's — measuring distortion
One number changed and the whole map moved — measuring distortion
The lines where the bending vanishes — measuring distortion
The area is unbiased and the perimeter is not — measuring distortion
The fourth number the ellipse does not carry — measuring distortion

31 August 2026

20 essays on paths and directions, the families, grids, and what a survey does, what each projection optimises, what is taught wrongly, what the numbers refer to, what a machine does with it and measuring distortion

The shortest route a vehicle can fly — paths and directions
The corner is not at the midpoint — the families
A family is not closed under averaging — the families
The network's answer is decided before it is measured — grids, and what a survey does
The threshold is not a percolation — what each projection optimises
Which small quantity the series is in — what is taught wrongly
A condition imposed at points is not a condition — what each projection optimises
A vertical rate needs a height system — what the numbers refer to
A cell's children do not fit inside it — what a machine does with it
Every country's zero is a different surface — what the numbers refer to
A label belongs to no tile — what a machine does with it
The parameters are not independent — what the numbers refer to
A ray from the centre hits the surface twice — what the numbers refer to
Which features survive is not a sample — what a machine does with it
Two routes to one scale — what a machine does with it
A choropleth is read by area — measuring distortion
A symbol has a size on the page and an area on the ground — measuring distortion
A dot map's density is partly the projection's — measuring distortion
The class breaks were computed on the page — measuring distortion
What the page cannot move — measuring distortion

30 August 2026

20 essays on paths and directions, the impossibility, the families, grids, and what a survey does, what is taught wrongly, what each projection optimises, what the numbers refer to, what a machine does with it and measuring distortion

A reach set with a cost that depends on direction — paths and directions
Four colours, and what a cut cannot do to them — the impossibility
The set that can be reached is not the set that can reach — paths and directions
Where the surface curves the other way — the impossibility
The gnomonic crosses a seam without a corner — the families
Further north on the grid is not further north — grids, and what a survey does
A rotation is not absorbed the way a shift is — what is taught wrongly
The basins have widths as well as depths — what each projection optimises
Which projection a weighting can make best — what is taught wrongly
The ground has an indicatrix too — what the numbers refer to
A velocity needs a frame and a strain rate does not — what the numbers refer to
A grid stops fitting the ground it was laid on — what the numbers refer to
The strain a map adds to the ground's — what the numbers refer to
The query a fast path actually answers — what a machine does with it
The cheapest map that meets its areas — measuring distortion
A density that asks for no room at all — measuring distortion
The ellipses are a sample, drawn at a size somebody chose — measuring distortion
The error that does not average down — measuring distortion
A length measured from noisy points is too long — measuring distortion
The best compromise for angle is not the best for bending — measuring distortion

28 August 2026

35 essays on paths and directions, the impossibility, grids, and what a survey does, the families, what each projection optimises, what is taught wrongly, what the numbers refer to, what a machine does with it and measuring distortion

A circle of a distance is not a circle — paths and directions
Nearest of many is a partition — paths and directions
A corridor has a width the page cannot keep — paths and directions
How many times, not whether — the impossibility
The places where a map is exactly right — the impossibility
Sixty zones was a decision about one latitude — grids, and what a survey does
What the net heuristic cannot find — the families
Where the valley breaks in two — what each projection optimises
The nearest map to an impossible request — what each projection optimises
The tolerance that decides the verdict — what is taught wrongly
The geoid model stops at a degree — what the numbers refer to
The attribute is a claim about the geometry — what a machine does with it
The second derivative cannot classify — measuring distortion
The error ellipse is not an ellipse — measuring distortion
Whether the ellipses point the same way — measuring distortion
The line drawn straight on the page is a route — paths and directions
A projection defined by a table has an interpolation in it — the families
The blunder the network cannot see — grids, and what a survey does
The datum hides inside the projection's parameters — what is taught wrongly
The height of the pass between two basins — what each projection optimises
The nearest equal-area map to an impossible request — what each projection optimises
A longitude that drifts with the rotation rate — what the numbers refer to
The rotation has two sign conventions — what the numbers refer to
The radius of curvature is two numbers — what the numbers refer to
The correlation is not the same in every direction — what the numbers refer to
A thousand features are wrong in the same direction — what a machine does with it
How many features a scale can carry — what a machine does with it
The answer depends on the cells it was counted in — what a machine does with it
A map drawn to a density it was handed — measuring distortion
The renderer runs out of numbers before the zoom does — what a machine does with it
Every density can be met and none is free — measuring distortion
A map that meets its target can fold — measuring distortion
Everything else on the page pays for the areas — measuring distortion
The light comes from a page direction — measuring distortion
The curvature of a field is not the curvature of its picture — measuring distortion

26 August 2026

15 essays on paths and directions, the impossibility, what is taught wrongly, the families, grids, and what a survey does, measuring distortion, what the numbers refer to and what a machine does with it

The shortest route is not at sea level — paths and directions
No map of the whole sphere is one to one — the impossibility
North cannot be up everywhere — the impossibility
Two opposite places on the same spot — the impossibility
The equator is not a circle either — what is taught wrongly
Where the control points are — what is taught wrongly
The family is a symmetry, not a shape — the families
The weights are a guess the solve believes — grids, and what a survey does
An average of ellipses is not an ellipse — measuring distortion
The slope of a field that was measured — measuring distortion
A long window and a square one — what the numbers refer to
What another common point buys — what the numbers refer to
When the edges do not line up — what a machine does with it
The road is drawn two pixels wide — what a machine does with it
A boundary that two features share — what a machine does with it

24 August 2026

15 essays on the impossibility, what is taught wrongly, measuring distortion, what each projection optimises, the families, grids, and what a survey does, what the numbers refer to and what a machine does with it

Impossible in two derivatives, possible in one — the impossibility
The projections that are beaten on both counts — what is taught wrongly
A slope is not a shape — measuring distortion
Not every distortion can be asked for — what each projection optimises
A net can land on top of itself — the families
The contour is right and the reading is wrong — measuring distortion
A grid reference names a square — grids, and what a survey does
The shape of the valley — what each projection optimises
Water runs downhill on the ground, not on the page — measuring distortion
The size at which the second derivative arrives — measuring distortion
The difference of two coordinates — measuring distortion
Cuts of the same size in different places — what the numbers refer to
A mountain is not a buried sphere — what the numbers refer to
A polygon on a sphere has no outside — what a machine does with it
The same number of cells, in two shapes — what a machine does with it

23 August 2026

15 essays on paths and directions, what is taught wrongly, the families, measuring distortion, what each projection optimises, grids, and what a survey does, what the numbers refer to and what a machine does with it

Where the shortest route stops being the only one — paths and directions
A residual has more than one explanation — what is taught wrongly
The inverse of the series is not the series of the inverse — the families
The indicatrix at a point that has none — measuring distortion
The developable surface was never necessary — the families
Report the map, not the parameters — what each projection optimises
A coordinate is the output of a solve — grids, and what a survey does
The seven parameters have their own uncertainty — what the numbers refer to
A vector tile has an integer grid — what a machine does with it
The map depends on where it was cut — what the numbers refer to
Cells that are rectangles in no coordinate — what a machine does with it
How far the plumb line bends — what the numbers refer to
A line has a length only at a scale — what a machine does with it
Simplification does not commute with the projection — what a machine does with it
A tolerance is a promise about the picture — what a machine does with it

22 August 2026

Two surfaces with the same curvature — the impossibility
The rule scored out of sample — what is taught wrongly
The second derivative is not an invariant — measuring distortion
When the answer is not in the library — what is taught wrongly
A coordinate is a number with a width — measuring distortion
An error ellipse is an indicatrix — measuring distortion
Every equal-area map is every other one — what each projection optimises
The net that loses the fewest neighbours — the families
The average of noisy positions moves — measuring distortion
The landscape the search walks on — what each projection optimises
The bound on the body the country is on — grids, and what a survey does
The line a height is measured along — what the numbers refer to
A conformal map of a body that is not a quadric — what the numbers refer to
A real edge has a width — what a machine does with it
The same data on two grids — what a machine does with it

20 August 2026

15 essays on paths and directions, what is taught wrongly, measuring distortion, the families, what each projection optimises, grids, and what a survey does, what the numbers refer to and what a machine does with it

The quickest route is not the shortest — paths and directions
The rule of thumb, scored — what is taught wrongly
A map does not say what it is — what is taught wrongly
Two projections that cannot be told apart — what is taught wrongly
What a careless copy hides — what is taught wrongly
A projection between two projections — measuring distortion
Where the series stops being the map — the families
The condition does not always decide the map — the families
The third parameter, run — what each projection optimises
The best grid a country could have had — grids, and what a survey does
The chain the satellite does not have — grids, and what a survey does
A chain of transformations does not close — what the numbers refer to
A conformal map of a body with three axes — what the numbers refer to
A tilted view has no zoom level — what a machine does with it
One edge is not an edge — what a machine does with it

19 August 2026

15 essays on the impossibility, what each projection optimises, measuring distortion, the families, what the numbers refer to and what a machine does with it

Curvature that varies from place to place — the impossibility
Solving for the map instead of choosing it — what each projection optimises
The second derivative over a region — measuring distortion
A conformal map onto a face — the families
A local model has an order — measuring distortion
A map with no formula — what each projection optimises
More faces, less distortion, more cutting — the families
The aspect has three numbers, not one — what each projection optimises
The sphere is not the plane at small counts — what each projection optimises
A map of a body with three axes — what the numbers refer to
A body with no sea level — what the numbers refer to
A query is a disc, and a disc is not a cell — what a machine does with it
A deflection is the slope of a mass — what the numbers refer to
The address is a curve through the sphere — what a machine does with it
An edge has no order of convergence — what a machine does with it

18 August 2026

15 essays on what each projection optimises, measuring distortion, the families, what the numbers refer to and what a machine does with it

A projection written as a condition — what each projection optimises
Tissot stops at the first derivative — measuring distortion
Bending and stretching are one failure — measuring distortion
The globe on a solid — the families
Three conditions are one too many — what each projection optimises
A map that cannot be read backwards — what each projection optimises
The cut has to go somewhere — the families
The second derivative has its own ranking — measuring distortion
What a face can preserve — the families
A coordinate on another body — what the numbers refer to
An address is an area — what a machine does with it
The same projection on a different body — what the numbers refer to
A body that is not an ellipsoid — what the numbers refer to
Hexagons cannot tile the sphere — what a machine does with it
A cell system trades area for shape — what a machine does with it

16 August 2026

15 essays on the impossibility, paths and directions, what each projection optimises, what is taught wrongly, measuring distortion, the families, grids, and what a survey does, what the numbers refer to and what a machine does with it

A direction carried round a loop — the impossibility
A route that must go round — paths and directions
The average of two projections — what each projection optimises
Equal-area on the wrong body — what is taught wrongly
How many sheets an atlas needs — what each projection optimises
The indicatrix is a limit — measuring distortion
The azimuthal family is one function — the families
The normal section is not the geodesic — what is taught wrongly
An area on the grid is not an area on the ground — grids, and what a survey does
Two parameter sets, one transformation — what the numbers refer to
Zoom is a ladder — what a machine does with it
A centroid belongs to a plane — what a machine does with it
A height that is not a length — what the numbers refer to
What a closed figure cannot see — grids, and what a survey does
Inside is a claim about the edges — what a machine does with it

15 August 2026

15 essays on what a machine does with it

A screen map is a pyramid of tiles — what a machine does with it
The scale of a screen map is not one number — what a machine does with it
A scale bar is right in one place — what a machine does with it
The square costs the poles — what a machine does with it
The pixel is a place with a size — what a machine does with it
A tile is drawn without its neighbours — what a machine does with it
The pyramid did not have to be Mercator — what a machine does with it
A coordinate without its system is not a location — what a machine does with it
A degree is not a unit of length — what a machine does with it
Computing an area needs a surface — what a machine does with it
A straight segment is a claim about a plane — what a machine does with it
The antimeridian is a cut in the numbers — what a machine does with it
Nearest is a question about the metric — what a machine does with it
Reprojecting a raster invents values — what a machine does with it
The operation decides the coordinate system — what a machine does with it

14 August 2026

15 essays on grids, and what a survey does

A grid has an origin that is not there — grids, and what a survey does
What a grid is made of — grids, and what a survey does
The scale factor of a line — grids, and what a survey does
The scale factor was chosen — grids, and what a survey does
The units are part of the coordinate — grids, and what a survey does
Designing a grid for one region — grids, and what a survey does
Where two zones meet — grids, and what a survey does
A grid scaled to the ground is not a map — grids, and what a survey does
What a tape measures — grids, and what a survey does
A traverse must close — grids, and what a survey does
The two ways to spread a misclosure — grids, and what a survey does
Setting out runs the chain backwards — grids, and what a survey does
Two grids over the same ground — grids, and what a survey does
The tolerance decides the model — grids, and what a survey does
A published coordinate is a result — grids, and what a survey does

11 August 2026

15 essays on what the numbers refer to

What a coordinate refers to — what the numbers refer to
The seven parameters, and what each one does — what the numbers refer to
A datum is fitted to a region — what the numbers refer to
Where a fit leaves residuals — what the numbers refer to
Molodensky's shortcut — what the numbers refer to
When a formula is not enough — what the numbers refer to
The epoch is part of the coordinate — what the numbers refer to
Height above what? — what the numbers refer to
The ellipsoid is a level surface — what the numbers refer to
A levelled height is not a distance — what the numbers refer to
The plumb line is not the normal — what the numbers refer to
The ground is not the grid — what the numbers refer to
The third coordinate moves too — what the numbers refer to
The flattening is not a free parameter — what the numbers refer to
The figure of the Earth was measured — what the numbers refer to

10 August 2026

12 essays on what each projection optimises, the impossibility, paths and directions, the families, measuring distortion and what is taught wrongly

Fitting the aspect to the region — what each projection optimises
How small is flat enough — the impossibility
The route with no shortest path — paths and directions
Choosing for a line, not a region — what each projection optimises
Flying a curve in straight legs — paths and directions
The conic is the whole family — the families
The curvature of the Earth is not one number — the impossibility
Where the worst point is — measuring distortion
Conformal does not mean the angles are right — what is taught wrongly
Distortion has a direction — measuring distortion
Where a pseudocylindrical puts its error — the families
Grid north is not north — the families

5–8 August 2026

34 essays on the families, what each projection optimises, the impossibility, paths and directions, measuring distortion and what is taught wrongly

Cylinders, cones and planes — the families
Every projection minimises something — what each projection optimises
No map is faithful — the impossibility
The shortest route is not straight — paths and directions
Tissot's indicatrix — measuring distortion
Web Mercator is not conformal — what is taught wrongly
Mercator against Peters — what is taught wrongly
What a standard parallel buys — the families
What can be unrolled — the impossibility
What survives a change of coordinates — measuring distortion
Which projection is best — what each projection optimises
Why Mercator exists — paths and directions
Compromise projections — what each projection optimises
The aspect is a free choice — the families
The gnomonic companion — paths and directions
The projection that shows true size — what is taught wrongly
The trade-off is two lines — the impossibility
The two ways a map is wrong — measuring distortion
Chebyshev's criterion — what each projection optimises
Measuring instead of naming — measuring distortion
The Earth is a sphere, and when it is not — what is taught wrongly
The great-circle vertex — paths and directions
Total curvature and the scale rule — the impossibility
Transverse Mercator and the series that computes it — the families
Geodesics on the ellipsoid, and why they are hard — paths and directions
Geodetic against geocentric latitude — what is taught wrongly
Giving up continuity — what each projection optimises
Measuring curvature from inside — the impossibility
Scale distortion is the third failure — measuring distortion
UTM and the zone system — the families
Datum shifts dwarf projection errors — what is taught wrongly
Distortion over a region — measuring distortion
The projections that gave up being one thing — the families
The plate carrée, the projection nobody chooses — what is taught wrongly

Every essay, by subject · by subject · by ladder · search