Find
Search the collection
Titles, summaries, fields, series and the named objects of every essay, searched as you type.
Material
- A crease that curves
- Four things that are not true
- One curve and one number
- Paper that stretches on purpose
- The crease has a radius
- The sculptors got there first
- What a flat sheet can become
- How many times can it be halved
- Where curved creases meet
- What one cut buys
- Bought with holes
- A curve has no panels
- The creases a sheet gives itself
- Every facet is a layer
- One cut short of falling apart
- A cut that removes no paper
- The crease that stops in the middle
- The sheet remembers
- A cut is a licence
- The decision a crumple has taken
- A cut is not local
- The crumple keeps its options
- How much line is on the paper
- Where the length sits
- A cut that reaches the edge
- The letters a crumple was given
- One cut removes one arc
- Rare is not hard
- A crumple has no tail
- The shortest crease is not a crease
- A count is not a length
- The fifth thing that is not true
- The gap between two curves
- Where the rulings run out
- A cut is surgery
- Two holes are two conditions
- A crease with no vertex to belong to
- The sixth thing that is not true
- The cut that changes nothing
- A tuck keeps what a gore cuts
- A straight tuck is a cone point
- Crowd the tucks toward the rim
- Crowding outward costs almost nothing
- Three answers, one count
- Where a ring of divisions belongs
- A length needs a scale
- The density a paper allows
- A paper limits spacing, not density
- A vertex creases the paper twice
- Only one side can run out
- An angle that turns faster than the crease
Design
- A flap costs a circle
- Designing on a grid
- Every flap on one axis
- From a packing to a crease pattern
- How much paper is wasted
- Packing is the hard part
- The last free parameter
- What joins the flaps
- The molecule that does not exist
- Bringing the other side to the front
- The square is a choice
- Paying in paper
- The corner is worth four times the middle
- What the grid settles
- The flap nobody holds
- Spelling a tree on a grid
- The whole alphabet of a grid
- Decided before the design
- The other grid
- Two packings, one radius
- The symmetry the letters cannot keep
- Spending the cheap paper
- The corner that splits the shrink
- A notch is not a hole
- A tree cannot argue
- What a grid costs in circuits
- The edge is what makes it hard
- Ninety-nine in a hundred pass
- A hole is cheap paper
- The designer's grid is the dearest thing here
- The edge was not what made it hard
- The second term
- The shapes the optimum has
- The skeleton changes its mind
- When symmetry costs
- Which side arrives
- A sheet with two edges
- The corner premium, with no corners
- A base needs an edge to point at
- A grid glued
- The symmetry a gluing adds
- A graft needs a square line
- Every pair, not every circle
- What the condition does not decide
- The price of a limb is not its length
- Six rectangles and one term
- A design that keeps its lines clear
- The width is charged in grid
- A price holds until the arrangement moves
- Rounding in the cheap direction
- One sheet down
Tessellation
- A material made of creases
- A property you can dial
- A sheet with one freedom
- A square that turns
- One vertex, repeated
- Patterns nobody designed
- Which polygons twist
- The base that tiles
- A unit that folds is not a tessellation
- What a corrugation costs
- The cylinder the pattern chooses
- A shrink is two numbers
- Where two twists share a pleat
- Fenced at both ends
- The corrugation that curves
- The propagation that never had to work
- The dial that decides nothing
- Thirty-two rules, one object
- The tiling the unit could not promise
- Cutting a patch out of a plane
- The property a patch does not have
- The paper a pattern asks for
- The ring is the loop
- A corrugation agrees with itself
- The rule that breaks the count
- Sixty-four rules, sixteen fold
- The loop is in the rule
- Four easy patches and one that is not
- Where a rule can close a loop
- The dial and the tiling that is not alike
- A corrugation never backtracks
- Any tiling makes a twist
- Folding it flat is one similarity
- Letters that agree get rarer
- Nothing to average over
- The Miura folds two ways
- The most decided vertex here
- Thirty-two rules, thirty-two pieces
- The corrugation that closes on itself
- One node per panel, with the rim gone
- The turn a column costs
- The period nobody measured
- A tessellation on a cylinder
- The seam that is not a symmetry
- A metamaterial with no edge
- Closing the loops is not folding
- One number where the corners wanted four
- The sheet draws in crooked
- The direction that gets longer
- Every twist writes an equilibrium
- The plane the five points were in
Rigid
- A state no motion reaches
- Folding that gets built
- Getting thickness round a corner
- Panels instead of paper
- Paper that folds itself
- The sheet has a thickness
- What the vertex does on the way
- Panels with somewhere to go
- Error is folded too
- Nowhere to put the error
- Paper through paper
- The only pattern that moves
- The vertex is geared
- The family the Miura belongs to
- Where an error goes
- The condition that is not flat-foldability
- One crease decides the sheet
- Thickness has a sign
- Solving every face at once
- Solved is not built
- Closing is not building
- A tolerance is a direction
- The pile, not the panel
- The allowance is spent at the end
- The hardest instant
- Fourth of eight, and still not chosen for it
- Two mechanisms at one point
- How deep is a crossing
- Two refusals that refuse differently
- Refused at one lettering
- The motion has no letters to choose
- A search with nothing to reorder
- A collision is an order
- An order with no least element
- Which crease to push
- Two panels that are one panel
- A mechanism that closes on itself
- The tube that gets built
- Thickness round a closed loop
- Three kinds of pile
- A panel is not the unit of depth
- Only four creases decide a Miura
- Two drivers and one freedom
- What a second deployment costs
- The crease count is a reliability budget
- The deciding set does not move
- Splitting a sheet buys area, not certainty
- The pattern cheapest to trust
- A gearing reflects stiffness squared
- A stub is never alone
- Two faults, not four
Flat-folding
- A strip is decidable
- How many assignments fold
- Local is not global
- One straight cut
- The gadgets that make it hard
- The smallest sector decides
- Two conditions at a point
- Which layer goes on top
- Why the difference is two
- The paper is all still there
- Almost every pattern fails
- Where the paper stops
- The lengths are free
- More than one way to lie flat
- Nothing meets at three
- A near miss is nearly as rare
- The outline is mostly crease
- Even is not enough
- Where the lemma says nothing
- The shadow does not name the pattern
- How little the conditions decide
- Crimp it away and ask again
- One marking, many objects
- The order does not name it either
- The order decides the count
- Which side is showing
- The creases that cannot move
- Nothing slides past anything
- A ring and a line
- The vertex the list does not have
- Two creases that cross
- Most of a patch is edge
- One cut for a star
- The lettering nobody could draw
- Which condition does the refusing
- One solution of a search nobody ran
- Every move leaves the verdict
- Twelve creases a micrometre long
- Where a sector crosses sixty
- One witness or forty
- A patch on a knife edge
- A region with no lettering
- The order that is its own mirror
- A contradiction is even
- A knife edge nine decimals wide
- A loop that goes somewhere
- A proof in one pass
- A sheet with no edge
- A tie is not a decision
- Consistent is not foldable
- No height to swap
- One step per panel is a table size
- Six creases and the same straight line
- The bottom layer is at the rim
- The crease the drawing cannot show
- The difficulty was in the coin
- The lettering that folds nowhere
- The lettering that was proved impossible
- The loop a vertex cannot close
- The loop is not the tangle
- The pieces without the list
- The rim is four letters a cell
- The rim lies over less
- The sheet has two sides
- The vertices nobody checks
- Walking between two foldings
- The seam carries a sign
- The band that needs an odd number
- Closure is not the identity
- Parity is not enough
- The triangle a strip becomes
- An alternating sum of angles
- How rare a band that folds is
- Half a rim
- The rim adds up
- Euler counts the gluing
- A grid that will not close
- A bottom layer on half a rim
- The arc that arrived twice
- The drawing does not say what is glued
Construction
- Dividing without measuring
- Folding a strip into thirds
- Folding beats the compass, by exactly one degree
- One fold at a time, and there are exactly seven of them
- The heptagon a compass cannot reach
- Where the cubic comes from
- Why the list stops at seven
- The eleven-sided one nobody can fold
- Two creases at once
- The largest triangle in a square
- The rectangle that keeps its shape
- A fold needs something to align
- One crossing, and then another
- One member of a family
- Cheap where it reaches
- What each axiom is worth
- The numbers a fold reaches
- Closer than a crease is wide
- Seven, and then twenty-two
- The sheet decides which points exist
- The grid a division makes
- An axiom may name no fold
- The edge was there first
- The axiom that names two folds
- How far from the nearest reference
- The third fold cannot be listed
- A hole is an edge
- Exact is not accurate
- The biggest one that can also be folded
- Which of the seven survive
- A reference on a sheet with no corner
- Dividing a loop into n
- The proportion a band asks for
- Reachable is not cheap
- The field has no edge
- How many polygons a fold reaches
- What buys the reach costs the accuracy
- Twenty-two is a floor
- The square is in the answer
- A construction assumes its sheet
- A stretch keeps crossings
- Every even polygon beats every odd one
- Each fold needs its own two
- Counting operations is not counting power
- A crease that does not exist yet
- Twos and threes run out
- Gauss's polygon is the expensive one
- The axiom that reaches furthest wastes most
- The crossing is as hard as the polygon
- The sheet a polygon fits exactly
- Turning is uphill all the way
- What the square saves
Complexity
- The fold a machine can make
- The patient machine is the weak one
- A machine that can only crimp
- Four questions about one sheet
- Hardness is about the worst one
- The answer is bigger than the question
- Where the exponent comes from
- What universality costs
- Getting close instead of getting it right
- The oldest open problem
- A no costs more than a yes
- Two directions that will not separate
- A short reason to say no
- Four ways to draw a pattern
- The cost is in the coincidences
- The count counts labels
- Where the machine catches up
- The order the refusals come in
- Drawn by the same hand
- The refusal that reads the list once
- A population that cannot fail
- Four populations with nothing to separate
- The test that never fires on a map
- A population nobody chose
- What a checker cannot check
- The machine that may choose
- Pruning on proofs alone
- Restarting what cannot be restarted
- Stopping is cheaper than finishing
- The cost of proving something false
- The map that is not a rectangle
- The order that proves nothing exists
- The patterns a checker is tested on
- What the rim was doing
- Where you cut hardly matters
- Which choice the cost lives in
- Which vertices are the random ones
- The map counted from the layers
- Half the slack
- Which pair is glued
- A proof in no nodes at all
- The cost of asking the wrong sheet
- One population, four sheets
- A map with no edges
- The tube a map makes
- Deciding is not making
- The easiest strip needs the deepest reach
- A shallow machine pays in states, not folds
- Fourteen states are one pile
- Each drawing has its own threshold
- The route, not the sheet
- The cheapest route crosses later
History
- Nothing here is as old as it sounds
- The oldest book cuts the paper
- The name is not the date
- Fifty years in the wrong language
- A record is not a proof
- A schoolteacher's theorem
- Found before it was designed
- The same vertex, found four times
- The star that was cut before it was proved
- From a shell to a solar array
- The paper had to arrive first
- Publishing the pattern instead of the sequence
- Two traditions and a merge
- The kindergarten was a geometry class
- What a dashed line can say
- The patterns nobody owns
- The half no notation records
- Two kinds of claim
- A file has no paper
- The reader decides the junction
- The file records no verdict
- The first thing about layers
- Half the recipe is decoration
- The cure was named first
- A test imported without its hypothesis
- Taught with a wrong reason
- The tail was named somewhere else
- Found by people not folding paper
- A theorem with an unstated hypothesis
- No format has a gluing
- A sheet has a size as well
- Which ceiling is binding
- How many wedges the paper allows
- Which cranes can stay joined
- When two of them are first attested together
- One lost source and the story changes
- Nearly every cutting fails at one crane
- A recipe needs degree four
- What the hindsight was worth
- The border is where the cranes come apart
- Two sentences for the Yoshimura
- The prediction held at eight and broke at ten
- The interval is wider than the number
- A question the record is too small to answer
- Some discoveries would make it worse
- A sheet is as large as two arms
- The paper that will not hold a crease
- Eighty layers and the sheet decides the rest
- A failure teaches a schedule nothing
- The field is empty where it would say nothing
- One choice with eleven answers
- The deepest point pays for the paper
Biology
- A crease carries no curvature
- A leaf packs by corrugating
- The bud chooses the pattern
- Opening with nothing to pull
- A wing that folds into nothing
- No motor in the fold
- Nothing in a body folds on a line
- Which way the disc curves
- The excess does not choose its waves
- A sheet that grows cannot lie flat
- How much surface fits in a body
- A sheet that routes itself
- Two things called folding
- The same corrugation in four places
- The organism is not the model
- Four finders, one option
- Twice as thick where it is thickest
- A leaf ends its pattern
- The taper decides nothing
- The leaf's rules are the Miura's
- The plant's pattern is not a hard case
- Nothing grown was cut out of anything
- Two ceilings
- Nothing grown has a seam
- The census returns one
- Four materials, four optima
- The number is the angle
- The surface has to be supplied
- Two surfaces in one box
- The container picks the member
- The test measures the rim
- The fold count sets the spring
- A corrugation has one resting state
- A row the route cannot leave
- Three marks see nothing
- The helix chooses the lattice
- A cut reads a slope
- A nest pays four a level
- The wall is the flat sheet
- A chain of vertices switches all at once
- Every cheap test misses a shape
- How far open is a question about the grip
- Springs that disagree do not offer a choice
- Standing up beats lying down by eight
- The channel grows with what it feeds
- A domain too short to be unique
- A test that only knows one lattice
- Holding a fold moves the force
- A loop takes choices away
- The angle the eight does not know
- In a tube the standing members lose
- The wedge belongs to one length