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Datums
- Cuts of the same size in different places
- When a formula is not enough
- The parameters are not independent
- The third coordinate moves too
- The radius of curvature is two numbers
- The figure of the Earth was measured
- The rotation has two sign conventions
- The plumb line is not the normal
- The ground has an indicatrix too
- Molodensky's shortcut
- A deflection is the slope of a mass
- A chain of transformations does not close
- A map of a body with three axes
- A mountain is not a buried sphere
- A datum is fitted to a region
- The flattening is not a free parameter
- A body that is not an ellipsoid
- The ground is not the grid
- The line a height is measured along
- A velocity needs a frame and a strain rate does not
- Where a fit leaves residuals
- A conformal map of a body that is not a quadric
- A longitude that drifts with the rotation rate
- A ray from the centre hits the surface twice
- A vertical rate needs a height system
- How far the plumb line bends
- Two parameter sets, one transformation
- The map depends on where it was cut
- The seven parameters, and what each one does
- A grid stops fitting the ground it was laid on
- What a coordinate refers to
- A conformal map of a body with three axes
- A levelled height is not a distance
- Every country's zero is a different surface
- Height above what?
- The ellipsoid is a level surface
- The correlation is not the same in every direction
- The strain a map adds to the ground's
- The same projection on a different body
- A height that is not a length
- The seven parameters have their own uncertainty
- A long window and a square one
- What another common point buys
- The epoch is part of the coordinate
- A coordinate on another body
- The geoid model stops at a degree
- A body with no sea level
- On a body with a hole, north can be up everywhere
- The height a coordinate does not carry
Wrong
- Two projections that cannot be told apart
- The equator is not a circle either
- The rule of thumb, scored
- The Earth is a sphere, and when it is not
- The answer is a set
- The datum hides inside the projection's parameters
- What a careless copy hides
- The rule scored out of sample
- The plate carrée, the projection nobody chooses
- A map does not say what it is
- Equal-area on the wrong body
- Where the control points are
- A residual has more than one explanation
- Conformal does not mean the angles are right
- Datum shifts dwarf projection errors
- Which small quantity the series is in
- The projections that are beaten on both counts
- The projection that shows true size
- Which projection a weighting can make best
- The normal section is not the geodesic
- Web Mercator is not conformal
- When the answer is not in the library
- A rotation is not absorbed the way a shift is
- Geodetic against geocentric latitude
- Mercator against Peters
- The tolerance that decides the verdict
- The ranking is not an order
- The average was a choice of norm
- The sheet moved before it was measured
- A map with no graticule
- An ellipsoid computed to a nanometre is known to a decimetre
- A compiled map agrees with its graticule except where it was copied
- A bearing on a sphere is decided by its latitude, not its radius
- An angle is a difference, and the difference doubles the error
- The correction is the smaller of the two corrections
- The area weighting was a readership all along
- A copy eased into place loses its seams before its source
- The region was a rectangle in a projection
- A residual cannot count the pieces of a map
- A strip of triangles carries the sphere's error to the next base
- An adjustment hides the sphere only in a strip of equal triangles
- A second tracing tells a drifting hand from a copied stretch
- An easing is a seam with a width, and a drifting hand hides the width
- Averaging tracings reads the easing, until the hand repeats itself
- The spread between hands charges the mean, and an office's habit hides in the sheet
- A known coast charges an office's habit, and a bending one takes it out
Impossibility
- No map of the whole sphere is one to one
- Four colours, and what a cut cannot do to them
- How big a triangle it takes
- Impossible in two derivatives, possible in one
- Measuring curvature from inside
- The places where a map is exactly right
- The trade-off is two lines
- A direction carried round a loop
- Where the surface curves the other way
- Two charts are enough, and one is not
- Two surfaces with the same curvature
- What can be unrolled
- Curvature that varies from place to place
- No map is faithful
- Total curvature and the scale rule
- Two opposite places on the same spot
- The curvature of the Earth is not one number
- How many times, not whether
- North cannot be up everywhere
- How small is flat enough
- What a cut buys
- How many triangles it takes
- Four cities that cannot be drawn to scale
- How wrong a flat picture has to be
- The best flat picture is not a map
- Five distances of six, and never more
- The escape is not a dimension
- A place with a size can be drawn to scale
- The error belongs to a few of the places
- A flat picture has one direction between two places, and the Earth has two
- A ring can be drawn whole, and only one way
- Five bearings of twelve, and only eight ways to draw them
- The pair that cannot be held is not the one the geometry names
- A mixed picture holds one more, and what it is holding is north
- The geoid has a curvature only if you say where you stopped
- Two numbers about the paper buy nothing about the places
- A second pin is a measurement of the places
- Two islands are three numbers, and the proof does not survive them
- A triangle reads the geoid's curvature, and that one converges
- One cut belongs to the island that would cost most alone
- A levelling loop reads the circulation, and the geoid has none
- The second cut goes across the sea
- A levelling loop weighs the root, and a triangle weighs the mountain
- A loop reads a root's depth from its own pattern, and a triangle reads none of it
- A sea with five islands is seldom worth five cuts
- Gravity is worth four loops a station, and the background still hides a deep root
Practice
- Setting out runs the chain backwards
- The chain the satellite does not have
- The scale factor was chosen
- The weights are a guess the solve believes
- A grid scaled to the ground is not a map
- Further north on the grid is not further north
- A traverse must close
- A grid reference names a square
- What a closed figure cannot see
- The tolerance decides the model
- Where two zones meet
- A coordinate is the output of a solve
- The blunder the network cannot see
- A published coordinate is a result
- The best grid a country could have had
- The bound on the body the country is on
- One pair of numbers, a hundred and twenty places
- Sixty zones was a decision about one latitude
- The scale factor of a line
- The units are part of the coordinate
- Two grids over the same ground
- A grid has an origin that is not there
- An area on the grid is not an area on the ground
- What a grid is made of
- Designing a grid for one region
- The two ways to spread a misclosure
- What a tape measures
- The network's answer is decided before it is measured
- One sentence, and the ground between its readings
- The line a commission can actually run
- A meridian boundary moves when its datum does
- An equidistance line belongs to a surface
- A tripoint defined three times
- A river boundary goes where the river goes, or stays where it was
- The sea is measured from a tide, and the headlands decide how much
- The highest summits stay where they are, and the watershed does not
- A straight baseline moves more water inward than sea outward
- The control carries the error of every network above it
- Three numbers are all a local survey can check of its control
- Naming the control station that moved takes a fifth
- Written in numbers, the archipelago rule still leaves eighteen
- Honest about its control, the test needs eight centimetres where it needed five
- The archipelago rule moves water between regimes, not between states
- One survey cannot tell an optimistic report from a moved mark
- An agency can map where its published covariance is optimistic
- Copied out to sea, a coast keeps its length and loses its bays
Families
- The aspect is a free choice
- A family is not closed under averaging
- UTM and the zone system
- Where a pseudocylindrical puts its error
- The cut has to go somewhere
- The projections that gave up being one thing
- The corner is not at the midpoint
- The developable surface was never necessary
- The inverse of the series is not the series of the inverse
- Transverse Mercator and the series that computes it
- What a face can preserve
- Where the series stops being the map
- More faces, less distortion, more cutting
- What the net heuristic cannot find
- The family is a symmetry, not a shape
- What a standard parallel buys
- A conformal map onto a face
- Cylinders, cones and planes
- The exact map says the seam is smooth
- A projection defined by a table has an interpolation in it
- A net can land on top of itself
- Grid north is not north
- The globe on a solid
- The condition does not always decide the map
- The net that loses the fewest neighbours
- The gnomonic crosses a seam without a corner
- The conic is the whole family
- The azimuthal family is one function
- Four radii of the Earth
- The span ladder, run on all five
- The corner that is the curvature
- A family is a function, not a list
- The maps with no family are simply better
- Joined where the parallels agree, and the meridians turn a corner
- The map is finer than the paper it is folded from
- An equal-area strip removes the corner and charges nothing for it
- Only Eckert II's family can be the strip, and its meridians are straight
- One curve beats the three maps it would replace
- The seam falls faster than the paper
- Scored lobe by lobe, the homolosine loses to its own lower half
- On the land it was drawn for, the homolosine wins by its meridians
- The land puts the homolosine's join eleven degrees higher
- The land would move Goode's lobes before his join
- The ocean centres its lobes on the land's cuts, and cannot keep its own cuts short
- The water would join Goode's map at seventy-five degrees
- A smooth curve beats the water's best join from its first term
Applied
- A thousand features are wrong in the same direction
- One edge is not an edge
- The attribute is a claim about the geometry
- Computing an area needs a surface
- The answer depends on the cells it was counted in
- The same number of cells, in two shapes
- The pixel is a place with a size
- Inside is a claim about the edges
- The square costs the poles
- A tile is drawn without its neighbours
- A vector tile has an integer grid
- Zoom is a ladder
- A boundary that two features share
- A degree is not a unit of length
- A screen map is a pyramid of tiles
- A line has a length only at a scale
- An edge has no order of convergence
- The operation decides the coordinate system
- A real edge has a width
- Reprojecting a raster invents values
- The pyramid did not have to be Mercator
- A cell system trades area for shape
- A coordinate without its system is not a location
- A tolerance is a promise about the picture
- The antimeridian is a cut in the numbers
- The road is drawn two pixels wide
- A query is a disc, and a disc is not a cell
- How many features a scale can carry
- When the edges do not line up
- A cell's children do not fit inside it
- A label belongs to no tile
- Hexagons cannot tile the sphere
- A polygon on a sphere has no outside
- A tolerance in map units is not a tolerance
- The address is a curve through the sphere
- The query a fast path actually answers
- A scale bar is right in one place
- An address is an area
- Two routes to one scale
- Simplification does not commute with the projection
- A centroid belongs to a plane
- The scale of a screen map is not one number
- The renderer runs out of numbers before the zoom does
- A tilted view has no zoom level
- Nearest is a question about the metric
- The same data on two grids
- Cells that are rectangles in no coordinate
- A straight segment is a claim about a plane
- Which features survive is not a sample
- The orientation is a policy
Choosing
- Not every distortion can be asked for
- Which projection is best
- Fitting the aspect to the region
- The height of the pass between two basins
- Solving for the map instead of choosing it
- The nearest equal-area map to an impossible request
- Compromise projections
- The nearest map to an impossible request
- How many sheets an atlas needs
- The first break is mostly its denominator
- Where the valley breaks in two
- Every equal-area map is every other one
- The average of two projections
- The sphere is not the plane at small counts
- A condition imposed at points is not a condition
- Three conditions are one too many
- The aspect has three numbers, not one
- Every projection minimises something
- Report the map, not the parameters
- The landscape the search walks on
- Choosing for a line, not a region
- Giving up continuity
- The threshold is not a percolation
- Chebyshev's criterion
- A map that cannot be read backwards
- The third parameter, run
- A map with no formula
- A projection written as a condition
- The nodes were evenly spaced
- The shape of the valley
- The pooled score abandons a region
- Chebyshev's map is the best at its worst, and not on average
- A criterion worth using is one whose answer is not unique
- The pass's depth belongs to the projection, and it is not a constant
- The pass that fails first is not the one that was measured
- Six projections have two curves, and the refusal has company
- A second clause decides the half that was already decided
- One exponent names one map, and at tight bands a better one than the band usually finds
- The sinusoidal is the edge of its family, not outside it
- The pass was a map meeting itself
- The basins have widths as well as depths
- Two maps and the line between them do the work of every exponent
- The band names the exponent for a compact region, and not for a thin one
- The map that keeps the most ground inside a tolerance
- Three maps make a plane, and the band's best map lies outside their triangle
- A cap on the worst departure keeps the thin regions' gain and gives back the square's
Distortion
- The light comes from a page direction
- The cheapest map that meets its areas
- The fourth number the ellipse does not carry
- The lines where the bending vanishes
- Bending and stretching are one failure
- Everything else on the page pays for the areas
- The indicatrix is a limit
- Distortion over a region
- The slope of a field that was measured
- A local model has an order
- The error that does not average down
- The second derivative over a region
- The second derivative is not an invariant
- The worst point is not on the grid
- One number changed and the whole map moved
- What the page cannot move
- A density that asks for no room at all
- Scale distortion is the third failure
- Tissot's indicatrix
- An error ellipse is an indicatrix
- The size at which the second derivative arrives
- The ellipses are a sample, drawn at a size somebody chose
- Water runs downhill on the ground, not on the page
- A map drawn to a density it was handed
- The error ellipse is not an ellipse
- Where the worst point is
- What survives a change of coordinates
- The indicatrix at a point that has none
- The difference of two coordinates
- The second derivative has its own ranking
- A choropleth is read by area
- A dot map's density is partly the projection's
- Tissot stops at the first derivative
- A symbol has a size on the page and an area on the ground
- Measuring instead of naming
- The area is unbiased and the perimeter is not
- Which of these numbers are the sampler's
- Every density can be met and none is free
- A mean that does not exist can still be printed
- The best compromise for angle is not the best for bending
- A coordinate is a number with a width
- The class breaks were computed on the page
- There is no equal-area lattice on a sphere
- The curvature of a field is not the curvature of its picture
- An average of ellipses is not an ellipse
- Distortion has a direction
- The average of noisy positions moves
- The contour is right and the reading is wrong
- Whether the ellipses point the same way
- A map that meets its target can fold
- A slope is not a shape
- The two ways a map is wrong
- The second derivative cannot classify
- A refinement that stops moving
- A projection between two projections
- A length measured from noisy points is too long
- The sample was drawn on the page
- Two indicatrices do not make a third
- A cartogram keeps the shapes it inflates
- A current drawn on a page has sources
- Rounding is not noise
Paths
- A route that must go round
- A reach set with a cost that depends on direction
- Where the shortest route stops being the only one
- The shortest route is not straight
- The set that can be reached is not the set that can reach
- A circle of a distance is not a circle
- The route with no shortest path
- Nearest of many is a partition
- The score is not stable at any scale
- Flying a curve in straight legs
- The great-circle vertex
- The shortest route a vehicle can fly
- The line drawn straight on the page is a route
- Geodesics on the ellipsoid, and why they are hard
- Why Mercator exists
- The shortest route is not at sea level
- The gnomonic companion
- The most compact shape depends on the paper
- The quickest route is not the shortest
- A corridor has a width the page cannot keep
- Every reach set ever drawn is too small
- A partition under a directed cost has two versions
- The shortest route between two coasts
- A crossing is a chain of decisions
- A drawn reach set stops at the river
- A crossing bends by a law only a conformal chart can show
- The rule that keeps a route near land is pinned at both ends
- The reach set takes the shape of the roads
- A jet moves the floor that a uniform wind cannot
- A diversion allowance in a wind is the same circle, moved upwind
- A line of position is Newton's method, but only on a conformal chart
- A cocked hat holds the ship one time in four
- The residual reports the error the fix was immune to
- What the extra unknown costs where nothing can see it
- A confidence ellipse is honest only where the sheet keeps angles
- A bend in the barrier puts the drawn polygon over water
- A streak along the jet moves the floor while the crossing is flown
- A low sight is worth keeping only if it is weighted
- Weighted by what it disagrees with, the fix trusts the sight it leans on
- A week of twilights learns what a sight is worth
- A forecast's error in where the streak is becomes a margin
- Tonight's residuals measure tonight's air badly and weight tonight's fix well
- A reach set drawn from the river's outline is a bound again
- An ensemble carries its own margin, if its spread is honest
- A layer is a meeting with the bank, not a corner turned
- A season learns the stretch from where the streak was, not from the floors
- A revised forecast is relearned in as many crossings as the learner remembers