Measured experiments in ancient architecture, with Greek words, Latin instructions, Akkadian measurements and the printed evidence.
Live workshop · PolyForm Noncommercial license
Fifteen problems you can inspect and measure:
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The arch and the pier: can every contact fit while friction still fails? Test the joints and bases separately.
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The Doric corner: which alignment gives way when columns and a triglyph frieze meet at a corner?
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The space between columns: why does Vitruvius leave a wider opening in the middle of an eustyle front?
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The curve inside the taper: how do Penrose's measured Parthenon offsets differ from a straight taper, a circle and his hyperbola predictions?
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The cut inside a column: why does a right-angle tool fit one prescribed flute but miss the other?
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The compass changes centre: can twelve circular arcs reach an Ionic volute's eye without turning in the same direction at every join? Draw your sequence, then inspect the source.
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Before the column stood: how can wheels carry a rectangular stone, and why does a geometric fit fail to explain a reported failed journey?
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The row that is not there: what happens to a temple's surrounding passage when an inner colonnade is omitted, and why do the text and apparatus disagree about the count?
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Twelve points. Two theatres.: how can three squares produce a larger orchestra and a shallower stage than four triangles drawn in the same starting circle?
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Thirteen vessels. Seven notes. Why does Vitruvius's pitch row turn upward on its way to the theatre's centre?
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Where you tie the rope: how does moving one tied end change the lift, with every wheel retained?
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One twelfth, seen from where?: does the same forward lean face every observer squarely?
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Eight channels. One revolution.: how does Vitruvius’s square grid become a spiral, and what makes its water stay inside?
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Seven names, one uneven obol: can a correct total recover the payments beside seven column-fluters’ names?
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A tower between two sources: how do a missing numerical row and a carved image produce different projections of Babylon’s Etemenanki?
A regular row of columns and a regular triglyph frieze cannot both keep their usual alignment at the corner when the beam is deeper than a triglyph is wide. Gonia lets you change that depth and see exactly what each architectural compromise preserves. It connects a geometric problem to the physical parts of a Greek temple and to Vitruvius's account of the difficulty.
The arch workshop starts
with an uncomfortable result: every joint contact fits, yet no choice of arch
force fits the selected pier bases. Widen each base from 0.5 to 1 half-span;
the existing trial then fits both checks while pier weight stays the same.
Choose Arch and pier from the root workshop, or open /gonia/arch.html
locally after the quickstart below. The original publication
records the earlier contact-only model. The finite-friction review
records the current addition and its separate publication boundary.
Change the circular rise, radial thickness, extra load and its position. Move the horizontal push and left bearing contact yourself. Ask for a path through the arch, then include the pier bases. The solver checks the complete admissible interval rather than treating a failed trial as proof of failure. A thin semicircle under its own weight supplies an infeasible example; a thick shallow ring exposes an unbounded ideal interval under unlimited compression. The automatic witness remains finite.
Now test a second assumption: can the contacts carry the shear? Choose Try a path that needs more friction. Every contact position fits, but the bearings require 0.655 while the chosen coefficient is 0.65. Ask for a whole path: a different thrust works. Set the coefficient to 0.60 and the complete joint-and-friction interval is empty. Try a sliding base isolates a different failure: increasing width cannot improve H/(V+P), while extra pier weight can. The two force-direction cones and signed force ledger show the difference. The coefficient is illustrative, not a measurement of ancient materials.
Source reads verify their exact recorded size and hash. Slow transfers can keep arriving beyond thirty seconds; a silent body stops after twenty seconds and an individual read has a three-minute ceiling. Cancel a reading save without stopping the source page you are reading. Changing source pages cancels the older transfer. Transfer and publication audit.
Search across every force and bearing position. The new comparison finds a numerical transition bracket separately for the arch joints and for the arch with its bases. Draw a witness at the feasible upper bound, then try the nearby failing coefficient. The force-versus-friction graph shows why the path with the least joint friction need not carry the bases. Its curves are illustrative; the solver checks complete intervals rather than sampling those curves.
Choose Compare a shallow arch with light piers. In that example, the arch-only transition lies between 0.0358428955078125 and 0.035843849182128906; including the bases puts it between 0.42659854888916016 and 0.42659950256347656. The two witnesses use different forces and bearing positions. Open Can a wider base change the best path? for a second experiment: widening keeps the current path's friction requirement unchanged, while allowing a different path with a lower requirement. In that example the better path actually has more thrust.
Save the geometry, full-precision bounds, conflicting constraints and witness settings as CSV. The illustrated reading retains the graph, both search results, and that same native CSV alongside the complete Latin source pages. Model and verification · Editable example · Search CSV · Script-free reading, gzip. Decompress the reading before opening it.
Open any of the fourteen joints in an enlarged view, or read all contacts as ordinary table values. Follow five Latin/English readings from Vitruvius VI.8.3-4, eight contextual word notes, and three complete pages of Krohn's 1912 edition. The ancient request for wider outer piers is kept separate from the modern force calculation and its assumptions. Sources and transcription record the actual print, original PDF identity and reproduction command.
The address keeps the current geometry, force, bearing, friction, inspected joint and printed page. An ordinary reload restores those choices online or offline; slider writes are coalesced and completed selections are flushed immediately, without adding a history entry for every movement. Save JSON and reopen it, export every joint to CSV, or keep a section SVG. The illustrated HTML retains the experiment, the actual source pages, fonts, complete licenses and native JSON/CSV/SVG/source-identity downloads. It needs neither scripts nor a connection. Current finite-friction examples include a 15-page reading; version 2 JSON keeps the chosen friction. Original version 1 records and full links reopen with their no-sliding assumption. The earlier contact-only files include a 14-page browser PDF and the compressed reading:
gzip -dc examples/arch/reading.html.gz > /tmp/gonia-arch-reading.htmlThe finite model uses thirteen rigid blocks with weight at their area centroids. It assumes no tension and unlimited compression. Sliding is either excluded by the original idealization or tested with uniform static Coulomb friction. The blue line joins interface resultants to guide the eye; it is not a continuous stress solution inside the stones. Pier width and weight are independent. No material strength, settlement or soil bearing is checked. Static friction adds a force inequality, not a simulation of motion following a failed check. This is an experiment in equilibrium, not a structural assessment or an ancient numerical design rule. Equations and limits.
The independent SciPy/HiGHS oracle balances each block's forces and moments using compressive endpoint forces, separate from the TypeScript interval solver. The reviewed 1,120 shape/load/friction cases cover 2,240 domains and 4,480 LP optimizations, with endpoint disagreement below 8e-14 W. Actual browser downloads are checked separately for equilibrium, source/font identity, complete passages, native reopening and PDF margins.
npm run check
npm run verify:arch
# With npm run preview in another terminal:
npm run test:arch -- http://127.0.0.1:4328/gonia/ /tmp/gonia-arch-review
python3 scripts/arch-artifacts.py /tmp/gonia-arch-reviewThe optional oracle uses uv and SciPy 1.18.1; artifact/PDF inspection uses
Python 3 and Poppler. Browser review uses Chromium and Firefox at 1440 and
375 pixels, including offline reloads of all fifteen rooms after worker takeover.
The PDF is untagged; physical printing and independent philological review
remain unverified.
Open the compass desk, or choose
Ionic volute from the root workshop. The publication record
records pushed source, canonical public bytes, actual downloads and offline
behavior separately from the earlier local review.
The source-transfer audit documents slow museum-photo
reading, bounded identity checks, independent cancellation and retry.
For local use, npm ci && npm run dev serves /gonia/volute.html.
Place twelve compass centres on the enlarged eye. Every command draws a real clockwise quarter circle and records your chosen pin, including repeated pins. The 1889 guide's complete sequence reaches the eye exactly, but its final direction changes by about 8.13°. Meeting at a point does not establish a shared tangent. Align one next centre and see its following endpoint move.
Read five Latin passages with new English, grammar notes and seven vocabulary notes. Six whole printed pages distinguish Vitruvius's instructions and textual problems from Juglaris and Locke's much later construction. A byte-identical museum photograph adds a surviving Ionic capital from Sardis, with restoration and uncertain original position retained in its note. The compass model is not fitted to that stone.
Keep editable JSON, exact-coordinate CSV, a physical-size SVG compass sheet with a 50 mm calibration bar, or one script-free illustrated reading with every source image, font and license. Reopen the pin sequence or copy an explicit drawing link. Source, geometry and limits.
Printable reading · Complete illustrated HTML, gzip · Editable drawing · Measurements · Physical compass sheet. Decompress the HTML before opening it.
Open the Babylon workshop, or use Babylon in the main workshop's navigation. The publication record separates the pushed source, public file identities, actual public downloads and offline behavior.
The Esagil tablet's numerical rows jump from the fifth storey to the seventh. Supply the conventional sixth level, change it, or leave it unknown. Without that supplied row, the 84 m subtotal does not establish an 84 m tower. Compare this scheme with a projection of the Tower of Babylon stele: the second terrace becomes 18 m in the conventional tablet reading and 9.516 m under the 91.5 m / 12.5 cm image calibration. Neither result is a survey of the built tower.
The room also tests the reported difference between the plan and elevation's scales. Inspect seven full source images, read the measurement words in Akkadian, or turn and relight the actual CC BY 4.0 photogrammetric stone scan. All 189,027 deposited triangles and their texture correspondences are retained; the stone's support is retained too. The photograph's lighting stays in its texture, and the plain geometry view uses a new illustrative light.
Save the numerical comparison as JSON, CSV or a self-contained SVG plate. The illustrated HTML keeps the current actual scan rendering when loaded, seven source images, the complete 2024 article, editable records, fonts and licenses. It opens and prints with scripts disabled. The history of the objects, a missing textual row, and a modern projection remain separate claims.
Source and model decisions · Learner workflow and retained evidence · Actual saved reading, gzip-compressed · Seventeen-page PDF.
Open the building-accounts room,
or use /gonia/ledger.html in the local development or production preview.
Two entries in the Erechtheion building accounts, 408/7 BCE, name the same
seven people. Their edited amounts sum to 90 and 100 drachmas. In each entry,
the difference between the largest and smallest payment is one obol.
Divide the total using the activity’s whole-obol rule, then reveal the record. Twenty-one arrangements balance the 100-drachma total; only one reproduces its seven amounts. A correct sum cannot tell you who received which extra obol, or why. Select each name to inspect the identifier, Greek numeral and corresponding band on the complete printed page.
The lesson distinguishes payments entered beside names from personal receipt or control of money. It follows current IG/AIO interpretations of ownership identifiers for enslaved workers, and leaves Kerdon’s status unspecified. Both entries belong to the same prytany; they are not a pair of daily wages. Restorations in the critical edition remain visible in the retained Greek XML and complete source scans.
Save a comparison as exact integer-obol CSV, or keep both entries, your allocation, four contextual Greek notes, all four source pages, fonts and licenses in one HTML reading. It opens and prints offline. Shared links and browser history preserve the entry, allocation, selected name and reveal state.
Source and design decisions · Learner workflow and local evidence · Actual saved reading · Printable PDF.
Unroll the shaft and follow one bucket. Six construction steps distinguish one blade's full pitch from eight blade starts. Compare the sixteen-digit source foot with a twelve-part reading, alter pitch and slope, and see where retained water stops touching the shaft or disappears. A complete tracked turn advances the bucket by one pitch without resetting it.
The Latin instruction supplies the proportions; an explicitly modern ideal analysis supplies water capacity. Compare water fraction with water per turn: a shorter pitch can fill a greater fraction while delivering less per revolution. Neither number is a claim about hydraulic efficiency or measured ancient output.
Twelve Latin readings with new English and word notes accompany five complete Krohn 1912 pages. Save a script-free illustrated reading with sources and fonts, an actual 24-page PDF example, numerical CSV and a one-pitch paper wrap for a 30 mm core. The wrap includes a 25 mm calibration bar; physical assembly has not been tested.
Source and model · Direct workflow and artifact review · Publication evidence.
Open the widened-metope example. The first panel is 2 triglyph widths wide; ordinary panels are 1.5. Choose Contract the end bay: the panels become equal, while the first column bay shrinks from 5 to 4.5. The corner triglyph remains 0.5 widths off its column axis.
Move the beam slider to 1. All three treatments now coincide. Move it back towards 3 and the conflict grows again. Open the plan to see the depth that the front elevation hides.
- Compare three treatments through linked, measured SVG drawings.
- Highlight a part and read its English, ancient Greek and Latin names.
- Read four sentences of Vitruvius IV.3.2 alongside a new English translation. The corresponding scanned pages are included.
- Copy a link to the selected geometry, or save a self-contained HTML study with both drawings, measurements, vocabulary and source passage.
- Use the workshop and source PDF offline after the footer confirms they are saved. No accounts, analytics, remote fonts or runtime services.
Open the viewpoint experiment. Vitruvius III.5.13 prescribes a forward inclination by one twelfth of a member's height. The new room asks which chosen observer that fixed lean faces squarely. At a 12 m face centre and 1.6 m eye, equal endpoint rays occur at 124.8 m; move farther and the upper ray becomes shorter. Those metres and that criterion belong to the modern model, not a viewing-distance rule in the text.
Compare vertical, prescribed, eye-facing and custom inclinations. Inspect a pinhole projection of equal physical divisions. Read six Latin clauses with new English, eighteen contextual word notes and two sourced Greek companions. Four complete printed pages retain the surrounding text and apparatus. An unchanged Met photograph locates an Ionic capital; its upper building is absent and its restored museum display supplies no measured tilt.
Save a script-free illustrated reading, SVG or comparative CSV. The retained twenty-page PDF preserves all 74 language fields and all five original JPEGs; the exact saved HTML is compressed for the repository. Decompress it before opening. All thirteen rooms share one integrity-checked offline edition. The independent geometry, actual browser files and interrupted nine-to-ten-room upgrades are recorded in the direct review and source/model analysis. The published edition has separate source, 91-file canonical and public-browser evidence.
The new hoist room follows Vitruvius X.2.1–3. Move the tied end from the lower block to the fixed support while keeping the same wheels: three upward tensions become two, or five become four. The latter routes are explicitly your alterations. The source supplies the route and names; the force law and SI dimensions are modern analysis.
Hold the rise constant to compare required rope, or hold the rope take-up constant and discover the smaller rise. Turn a chosen windlass with a longer arm: hand force falls, hand path grows, and ideal work agrees at the load, rope and hand. White dots follow material positions along the actual rope.
The loss extension asks a second question: does 90% at each wheel mean 90% for the whole machine? Set the three-wheel source route to the chosen 90% tension transfer. The supporting pulls become unequal, and whole efficiency is 81.3%. A 600 N load raised one metre takes about 738.007 J of input work; 600 J lifts it and 138.007 J is dissipated. Switch to five wheels: less hand force, more total work in this stated modern raising model.
After starting locally, open hoist.html#hw-losses and choose Try three wheels
at 90%. The wheel ledger follows tensions and rope travel relative to each
axle. The first upper wheel on the fixed-tie route does not turn and is assigned
zero resisting torque. The windlass stays ideal; no ancient efficiency,
starting friction or lowering behavior is inferred. The percentage, complete
ledger and work division travel with JSON, CSV, SVG and the illustrated study.
Older records reopen at the original ideal setting.
Model and exact assumptions · Local browser and source review · Actual saved reading, gzip · Printed reading · Measurement CSV. The independent follow-up audit reproduces damaged-cache readiness and server-maintenance failures, adds a byte-checked repair action in all fifteen rooms, and makes an interrupted hoist save cancellable. Its shared slow-transfer review also exercises native worker interruption and recovery. The current retained reading, 15-page PDF, and measurements keep the license notices with the source and calculation. Hosted delivery is checked separately.
Seven excerpts with new English, twenty-eight contextual Latin and Greek notes, five complete printed pages and visible editorial additions connect the model to Krohn's 1912 text. Save a complete script-free illustrated reading, SVG, 211-row CSV or strict editable JSON; reopen settings and share a link. The repository retains a 13-page PDF printed from the actual saved reading. That earlier nine-room production edition was cached with file-integrity checks.
Source and model · Direct review. The earlier nine-room publication record is retained. Publication evidence identifies all 81 canonical hosted files and the separate public browser review.
Open the sounding-vessel workshop. The earlier eight-room publication has a retained 72-file identity record; Chromium and Firefox checks cover desktop and phone controls, audio downloads, saved readings and navigation through that edition offline. Public review · Model and review.
Vitruvius V.5.2 assigns seven pitches to thirteen positions. From either end, the pitches descend twice, then rise from paramese to nete synhemmenon. The fourth placement is not another musical fourth. Select and hear the pairs, then sort each half by pitch to see exactly which vessels your alteration moves.
A separate resonance experiment asks what matching a frequency can establish. Detune a driving tone and hear the response diminish at a fixed playback gain. Change damping to compare a narrow steady response with slower build-up during a short burst. The model shows its equation and time trace; it makes no claim to reproduce an ancient vessel or improve a theatre's acoustics.
- Read nine Latin excerpts with new English and language notes; inspect five complete printed pages, including their critical apparatus.
- Follow Greek note names, the mounting instruction, and Vitruvius's distinction between local examples and reported evidence.
- Save an illustrated reading with both sounds, all scans and fonts embedded, or export the plan, measurements and WAV files separately.
- Use all eight rooms offline after the edition is saved. Playback stops on control changes, history navigation, a hidden tab, or a Stop action.
Saved reading · Printable PDF · Row sound · Matched response · Detuned response · Source and model.
Open the theatre drawing room. Follow five construction stages in Vitruvius V.6–7. Trace the Roman triangles and Greek squares, place the two stage lines, and move the Greek compass from the centre to the opposite ends of the diameter. The lower arcs have radius 2R, not R. A movable cross-section makes their small extra side strips visible.
At a chosen 20-metre diameter:
| Construction | Stage depth | Constructed orchestra area |
|---|---|---|
| Roman, four triangles | 5.00 m | 157.08 m² |
| Greek, three squares and three centres | 2.93 m | 292.49 m² |
| Greek stage lines with a one-circle alteration | 2.93 m | 285.62 m² |
The alteration isolates the consequence of skipping the compass instruction. It is not presented as another historical plan. The text's vertical limits remain separate: at most five source feet for the Roman platform, ten to twelve for the Greek. No ancient foot conversion is assumed.
Read ten Latin excerpts with new English and grammar; inspect five full printed pages, including the left/right variant in the apparatus. Compare two later historical interpretations. Share the construction or save its SVG, coordinates and a complete illustrated reading. The seven-room app works offline after its edition is saved.
Portable HTML · 17-page PDF · SVG drawing · Coordinates · Model and sources · Review.
These are ideal textual plans. Seating bands and stage side edges are illustrative. Areas predict no audience capacity, acoustics or structural safety.
Open the temple-plan room. Original review · Current publication evidence.
Keep the outer row and simplified cella block fixed. Choose Keep both rings, then Omit the inner ring. At the chosen 2.25-diameter clear gap, two narrow lanes and the former shaft position join into a 5.5-diameter strip. A separate detail measures between shaft faces, rather than confusing clear gaps with axis pitches. Phones receive a complete upright plan and passage detail.
Trace the outer or inner ring one position at a time. Eight across an end and fifteen along a flank describe a boundary, not a filled grid. Corners count once:
| Model ring | Ends, including corners | Flanks, excluding corners | Total |
|---|---|---|---|
| Outer | 2 × 8 | 2 × 13 | 42 |
| Inner | 2 × 6 | 2 × 11 | 34 |
Vitruvius's editor prints 34 removed columns, but the apparatus records 38. The workshop exposes the discrepancy; a regular grid cannot settle the textual or archaeological question. Read five Latin excerpts with six grammar notes, connect Greek headwords to parts, and enlarge the actual apparatus entry. Compare the 1904 excavation publication's preserved-state plan, proposed restoration and capital photograph. The restored temple has porch and interior columns beyond the model's rings.
Save all 76 potential ring positions as CSV, including present/omitted flags, or save an illustrated reading with both arrangements, fonts, licenses and all five complete source images embedded and verified by SHA-256. Offline HTML reading · Printable PDF · Coordinates · Model and source decisions.
This is a regular geometric experiment in shaft diameters. It omits bases, porches, interior columns, steps and roof supports. It computes no crowd capacity, structural adequacy, price or measured Magnesia reconstruction.
Open the six-column eustyle front.
Its six columns, four ordinary gaps and central opening add up to eighteen
lower diameters: 6 + 4 × 2.25 + 3 = 18. At an 18-metre front, each lower
diameter is therefore 1 metre.
Select Try making every gap equal. Keeping the front fixed increases the diameter to about 1.043 metres. Hold the diameter at 1 metre instead and the front contracts to 17.25 metres. The drawing, comparison, shared link and saved reading identify this as your alteration of the ancient prescription.
Compare all five spacing systems at a common drawing scale; change between four, six and eight columns; distinguish clear intervals from axis-to-axis bays. Read the Latin, learn six Greek word-parts, and inspect the four bundled pages of Krohn's 1912 edition. The HTML download includes the actual page images and opens offline. Araeostyle spacing remains a chosen illustration: the cited passage supplies no fixed numerical gap.
| System | Ordinary clear gap / D | Central gap / D | Height / D |
|---|---|---|---|
| Pycnostyle | 1.5 | 1.5 | 10 |
| Systyle | 2 | 2 | 9.5 |
| Eustyle | 2.25 | 3 | 9.5 |
| Diastyle | 3 | 3 | 8.5 |
| Araeostyle | Chosen example | Chosen example | 8 |
These are Vitruvius's idealized instructions before his later corner-thickening adjustment, not measurements of a named temple. Metres provide a modern scale. The model omits structural loads, entasis and measured base/capital profiles. Review and reproducible evidence · Saved illustrated reading · Six-page PDF.
Open the entasis workshop. The Parthenon edge is drawn at equal horizontal and vertical scales. Beside it, a second drawing subtracts the straight endpoint taper and enlarges the small outward departures. Select one of five printed heights to connect the point, original offset, calculation and table row.
At 15.75 feet, straight taper gives 0.342762 feet inward; Penrose's corrected column offset is 0.2886 feet. The difference is 16.508 mm outward from that taper. It remains inward of the base: entasis need not make a column wider than its bottom.
Compare Penrose's printed circle and hyperbola predictions. The circle passes through the base, middle and top by construction; inspect the other two rows instead of mistaking those three agreements for independent evidence. The hyperbola's printed middle row differs by 0.0011 feet, although Penrose's prose says the differences do not exceed 0.001. Both readings remain visible.
The workshop also compares six reported maxima at actual size and equal shaft length, reads Vitruvius III.3.13 with Greek and Latin vocabulary, and includes five complete source images. Download the numerical CSV or a self-contained illustrated reading; all rooms and their source packets are available offline after the footer confirms the complete edition.
The five points do not establish a continuous measured profile, an ancient construction method or an optical effect. Source decisions and the reviewed browser and source evidence explain these boundaries. The drawings join stations with explicit guides; they do not invent intermediate observations.
A saved circle comparison and its eight-page PDF include all five scans. Extract the gzip HTML before opening; it retains the original captured reading bytes.
Open the flute workshop. Keep a groove 100 mm wide, and move the corner of a right-angle tool along it. The Doric square-and-compass construction gives a quarter-circle hollow; Vitruvius's Ionic moving-square test is consistent with a semicircle.
| Same 100 mm chord | Hollow depth | Angle from P to both edges | Second tool contact at midpoint |
|---|---|---|---|
| Doric compass construction | 20.710678 mm | 135 degrees | 41.421356 mm short of B |
| Ionic semicircle | 50 mm | 90 degrees | Meets B |
| Doric flat-faced alternative | 0 mm | Collinear; no hollow | Not a hollow-gauge test |
Repeat the actual concave arcs around a 20- or 24-division shaft. Choose an illustrative Ionic fillet width; compare the removed area and shaft diameter while keeping the groove chord fixed. These are model dimensions and source prescriptions, not measured profiles or structural predictions.
Download a millimetre-scaled SVG with a 25 mm calibration bar, or a self-contained illustrated reading with all three complete source pages, fonts, Latin grammar and Aristotle's Greek nested genitives. Its embedded CSV and SVG downloads work from a native offline file. Physical printer scaling remains unverified; the generated PDF's bar measures 24.999824 mm.
Source decisions · Review · Saved reading · Original carving PDF · Paper template · Coordinates
Open the two-segment comparison. The same chord divides one circle into two regions. Move P in the hollow and Q on the other arc. Green identifies the region containing the point; orange marks the arc facing it. In the Doric circle, P keeps 135 degrees and Q keeps 45. In the Ionic circle, both keep 90.
Two isosceles triangles explain P's angle as a sum of changing base angles. The cyclic quadrilateral explains why Q is supplementary. Read Euclid III.31's Greek beside Heiberg's explicitly modern Latin translation and a new English translation. Learn how “in the larger segment” can describe the smaller angle, and why “angle in a segment” differs from “angle of a segment.”
The companion CSV records both points on both arcs. The new portable reading includes both diagrams, the calculation, all five full source pages, fonts, licenses and a working download of those comparison coordinates. The original carving reading is retained as its reviewed earlier edition.
Source decisions · Review · Complete reading · Printable PDF · Both-arc coordinates
Roll the stone. Compare a circular shaft, a bare rectangular stone and a stone turning inside wheels. The end view follows the centre while the road ruler moves beneath it. The height graph exposes the difference between rolling on a circle and tipping about successive corners.
| Chosen 8 × 6 section | Centre height | Minimum full-turn clearance |
|---|---|---|
| Bare rectangle | Rises and falls between 3 and 5 | Touches the road while tipping |
| Radius-6 wheels | Constant 6 | 1 |
| Radius-4 wheels | Attempted constant 4 | -1; blocked between the quarter-turns |
The bare rectangle is a modern counterexample, not a prescribed ancient method. The source gives no cross-section for Metagenes's beams; these initial dimensions are chosen. Try a wheel that is too small: it clears at 0° and 90° but intersects the road in between. The red region shows the obstruction instead of presenting that attempted motion as physically possible.
Paconius's reported dimensions give an 8 × 6 end section, a five-foot half-diagonal and a 7½-foot wheel radius under the stated diameter/axis readings. The resulting 2½ source feet of clearance do not explain why, according to Vitruvius, the rope-driven machine veered and had to be pulled back. This model supplies no steering, soil or force estimate.
Five Latin excerpts, nine selectable grammar notes and three Greek technical headwords explain pivots, bearing rings, rollers and architraves. Complete Krohn pages 230–231 include the critical apparatus and the gap in the frame description. Enlarge and pan either the diagram or the original print. Keep a shared pose, download the selected position plus all 361 full-turn samples, or save an illustrated reading with both source pages, fonts and licenses embedded. All rooms are available in the complete offline edition.
The transport model gives the geometric derivation, source readings and limits. Its independent checker moves a complete polygon around successive support vertices; it does not import the app's formula.
npm run verify:transport
npm run test:transport -- /tmp/gonia-transport
node --import tsx scripts/transport-cases.ts | python3 scripts/transport-oracle.py /tmp/gonia-transport/review.json
python3 scripts/transport-source-review.pyBuild first and keep dist/ unchanged during the browser review. It uses
installed Playwright Chromium and Firefox, and opens actual native downloads.
The source reviewer requires Poppler and verifies the identified original PDF
and the bundled two-page PDF against the exact JPEGs. Supply --pdf <path> to
use an existing copy of that original. The source manifest
records all identities and the Greek dictionary entries.
The transport review retains the public browser, source, print and clean-install evidence. Try the actual saved reading, seven-page A4 PDF and complete-turn CSV.
Node 24 or newer:
git clone https://github.com/antonsoo/gonia.git
cd gonia && npm ci
npm run devOpen http://127.0.0.1:4328/gonia/. npm run build produces the static site in
dist/; npm run preview serves that build at the same address.
The outer corner is the origin. A corner column centred under two perpendicular beams lies half a beam depth from each face. A triglyph flush with that corner has its centre half a triglyph width from the edge.
Corner face Flush triglyph centre Corner column axis
0 ---------------- T/2 ---------------------- B/2
<---- discrepancy ---->
discrepancy = (B - T) / 2
normal column bay = 2 * (triglyph width + metope width) = 5 T
For the default B = 2T:
| Treatment | End metope | End bay, axis to axis | Strip before triglyph | Corner triglyph off-axis |
|---|---|---|---|---|
| Keep centres aligned | 1.5 T | 5 T | 0.5 T | 0 T |
| Widen end metope | 2 T | 5 T | 0 T | 0.5 T |
| Contract end bay | 1.5 T | 4.5 T | 0 T | 0.5 T |
The pure geometry is in src/core/corner.ts. Drawings,
interface and exports consume the same coordinates. Share state is bounded
and carried in query parameters, so links to sections do not erase it.
The build creates an offline cache with integrity checks for every saved file.
An independent Python solver sets up eight positional constraints using exact
rational arithmetic, solves for the column and triglyph positions, then measures
the resulting gaps and widths. Across all 603 supported depth/treatment
combinations it checked 9,648 coordinates and distances; the largest difference
was 1.7763568394002505e-15 T, below a 1e-12 T tolerance.
See docs/geometry-review.json.
The browser review exercises real keyboard controls, all treatments and vocabulary entries, source-to-drawing links, exported documents, and offline reloads with the origin's sockets actually disabled. It runs in Chromium and Firefox at 1440 and 375 pixels and includes automated accessibility checks. See verification notes for the reviewed revision and the scope of those results. These checks establish the application's behavior, not historical certainty.
The corner workshop is an idealized local corner, not a reconstruction of a named building. It uses one intermediate triglyph per normal column bay and square ordinary metopes. Column profiles are illustrative. Roof, sculpture, colour, entasis, load calculations and whole-building refinements are omitted. The equal-width endpoint is a geometric limit, not proof of a historical timber construction.
Vitruvius's half-triglyph adjustment agrees with the model at B = 2T; it is not the discrepancy at every beam depth. His full prescribed temple scheme is not reproduced here. The source reader keeps his criticism separate from the modern geometric explanation.
- Vitruvius, De architectura IV.3.2, ed. F. Krohn (Teubner, 1912), pp. 82–83. Archive scan.
- Vitruvius, De architectura III.3.2–10, same edition, pp. 64–67. Archive scan. Height follows the explicit nine-and-a-half reading in III.3.10.
- Francis Penrose, An Investigation of the Principles of Athenian Architecture, second edition (1888), pp. 39–41 and plate XIV. Heidelberg scan. Five corrected offsets and two sets of predictions come from p. 41; six reported maxima and shaft lengths come from p. 40.
- Vitruvius, De architectura III.3.13, Krohn (1912), p. 68. Archive scan.
- Alain Goriely, “The illusion of illusions: There are no optical corrections in the Parthenon,” 2026 analysis. Linked as a contrasting interpretation; its figures are not reused.
- Mark Wilson Jones, “Doric Measure and Architectural Design 2: A Modular Reading of the Classical Temple,” AJA 105.4 (2001), 675–713, especially fig. 2, p. 677. DOI.
- Greek vocabulary checked against LSJ / Perseus; individual entries are linked in the workshop. Material provenance and licenses.
npm run check
npm run verify:geometry
npm run verify:spacing
npm run verify:entasis
npm run verify:fluting
npm run verify:segments
npm run verify:colonnade
npm run test:colonnade -- /tmp/gonia-colonnade-review
npm run test:browser -- /tmp/gonia-browser-review.json
npm run test:spacing -- /tmp/gonia-spacing-review/browser.json
python3 scripts/spacing-oracle.py /tmp/gonia-spacing-review/browser.json
npm run test:entasis -- /tmp/gonia-entasis-review/browser.json
python3 scripts/entasis-oracle.py /tmp/gonia-entasis-review/browser.json
npm run test:fluting -- /tmp/gonia-fluting-review
python3 scripts/fluting-oracle.py /tmp/gonia-fluting-review/browser.json
# With npm run preview in another terminal:
npm run test:segments -- http://127.0.0.1:4328/gonia/ /tmp/gonia-segments-review
python3 scripts/segments-oracle.py /tmp/gonia-segments-review/browser.json
# Optional native PDF inspection (requires uv):
uv run scripts/fluting-print-review.py /tmp/gonia-fluting-reviewThe independent oracle requires Python 3. The browser review requires
Playwright Chromium and Firefox; install them with
npx playwright install chromium firefox if needed.
It serves dist/ itself and writes its screenshots and saved documents beside
the requested report.
Contributing explains the source and review standards.
New versions are released under the PolyForm Noncommercial License 1.0.0. It is free for any noncommercial purpose, including personal study, teaching and research, and for use by charities, schools, universities, research organizations and government institutions. Commercial use needs written permission from Anthony Mercer (anthony@praviel.com). Versions up to commit dcc8866 (2026-11-01) were released under the MIT License, and copies of those versions keep it.
Code, original drawings and translations: PolyForm Noncommercial 1.0.0, Anthony Mercer, 2026. Source scans and fonts have the terms described in THIRD_PARTY.md.
The retained-source development review records Node 24 quickstarts, raw/downloaded JSON identity, source edit/restoration and complete study downloads without Vite public-import warnings.
The arch workshop is published and independently reviewed, with canonical hosted-byte, real browser, offline and native-file receipts.
The hoist loss and offline audit publication records the current hosted edition and all 15 public architecture rooms.