Explore exact rationals

Navigate the Stern–Brocot tree, inspect each node's exact structure, and evaluate a RiX formula at the selected rational.

← All RiX showcases

Move through the tree

Every step is computed from the exact structural fraction.

↑ Parent
← Left child
Right child →
Root

Jump and compare

Jump accepts a RiX fraction expression. Formula is plain RiX source evaluated with exact x in a fresh scope.

Hold ↓ for decimal labelsArrowDownReleasedDisplay only: the exact fraction and formula values do not change.
Coordinates use nearest rounding at 6 decimal places. 0 numeric values were approximated; 0 distinct-value collision sets. Exact geometry uses outward enclosure with radius 0 SVG user units; this guarantee does not certify approximate inputs. No explicit clip regions; SVG overflow remains visible. Graphic size 1: source 600; displayed 600; bounds 600 to 600 Graphic size 2: source 400; displayed 400; bounds 400 to 400 Path point 1 x: source 300; displayed 300; bounds 300 to 300 Path point 1 y: source 106; displayed 106; bounds 106 to 106 Path point 2 x: source 90; displayed 90; bounds 90 to 90 Path point 2 y: source 208; displayed 208; bounds 208 to 208 Path stroke width: source 3; displayed 3; bounds 3 to 3 Path point 1 x: source 300; displayed 300; bounds 300 to 300 Path point 1 y: source 106; displayed 106; bounds 106 to 106 Path point 2 x: source 510; displayed 510; bounds 510 to 510 Path point 2 y: source 208; displayed 208; bounds 208 to 208 Path stroke width: source 3; displayed 3; bounds 3 to 3 TextMark position x: source 300; displayed 300; bounds 300 to 300 TextMark position y: source 50; displayed 50; bounds 50 to 50 TextMark size: source 12; displayed 12; bounds 12 to 12 Rectangle origin x: source 242; displayed 242; bounds 242 to 242 Rectangle origin y: source 59; displayed 59; bounds 59 to 59 Rectangle size x: source 116; displayed 116; bounds 116 to 116 Rectangle size y: source 46; displayed 46; bounds 46 to 46 Path stroke width: source 2; displayed 2; bounds 2 to 2 TextMark position x: source 300; displayed 300; bounds 300 to 300 TextMark position y: source 88; displayed 88; bounds 88 to 88 TextMark size: source 18; displayed 18; bounds 18 to 18 TextMark position x: source 90; displayed 90; bounds 90 to 90 TextMark position y: source 200; displayed 200; bounds 200 to 200 TextMark size: source 12; displayed 12; bounds 12 to 12 Rectangle origin x: source 32; displayed 32; bounds 32 to 32 Rectangle origin y: source 209; displayed 209; bounds 209 to 209 Rectangle size x: source 116; displayed 116; bounds 116 to 116 Rectangle size y: source 46; displayed 46; bounds 46 to 46 Path stroke width: source 2; displayed 2; bounds 2 to 2 TextMark position x: source 90; displayed 90; bounds 90 to 90 TextMark position y: source 238; displayed 238; bounds 238 to 238 TextMark size: source 18; displayed 18; bounds 18 to 18 TextMark position x: source 510; displayed 510; bounds 510 to 510 TextMark position y: source 200; displayed 200; bounds 200 to 200 TextMark size: source 12; displayed 12; bounds 12 to 12 Rectangle origin x: source 452; displayed 452; bounds 452 to 452 Rectangle origin y: source 209; displayed 209; bounds 209 to 209 Rectangle size x: source 116; displayed 116; bounds 116 to 116 Rectangle size y: source 46; displayed 46; bounds 46 to 46 Path stroke width: source 2; displayed 2; bounds 2 to 2 TextMark position x: source 510; displayed 510; bounds 510 to 510 TextMark position y: source 238; displayed 238; bounds 238 to 238 TextMark size: source 18; displayed 18; bounds 18 to 18 TextMark position x: source 300; displayed 300; bounds 300 to 300 TextMark position y: source 328; displayed 328; bounds 328 to 328 TextMark size: source 12; displayed 12; bounds 12 to 12 Rectangle origin x: source 170; displayed 170; bounds 170 to 170 Rectangle origin y: source 338; displayed 338; bounds 338 to 338 Rectangle size x: source 260; displayed 260; bounds 260 to 260 Rectangle size y: source 48; displayed 48; bounds 48 to 48 Path stroke width: source 2; displayed 2; bounds 2 to 2 TextMark position x: source 300; displayed 300; bounds 300 to 300 TextMark position y: source 368; displayed 368; bounds 368 to 368 TextMark size: source 16; displayed 16; bounds 16 to 16{"schema":"rix.svg.coordinate-lowering@1","precision":6,"rounding":"nearest","fontPolicy":"system","requestedFonts":[],"definitions":[],"guarantee":"outward-exact-enclosure","enclosureRadius":0,"approximated":0,"entries":[{"path":"Graphic size 1","role":"width","exact":"600","lowered":"600","lower":"600","upper":"600","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Graphic size 2","role":"height","exact":"400","lowered":"400","lower":"400","upper":"400","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Path point 1 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size","role":"font-size","exact":"12","lowered":"12","lower":"12","upper":"12","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin x","role":"x","exact":"242","lowered":"242","lower":"242","upper":"242","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin y","role":"y","exact":"59","lowered":"59","lower":"59","upper":"59","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size x","role":"width","exact":"116","lowered":"116","lower":"116","upper":"116","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size y","role":"height","exact":"46","lowered":"46","lower":"46","upper":"46","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Path stroke width","role":"width","exact":"2","lowered":"2","lower":"2","upper":"2","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"300","lowered":"300","lower":"300","upper":"300","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"88","lowered":"88","lower":"88","upper":"88","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"18","lowered":"18","lower":"18","upper":"18","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"90","lowered":"90","lower":"90","upper":"90","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"200","lowered":"200","lower":"200","upper":"200","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"12","lowered":"12","lower":"12","upper":"12","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin x","role":"x","exact":"32","lowered":"32","lower":"32","upper":"32","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin y","role":"y","exact":"209","lowered":"209","lower":"209","upper":"209","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size x","role":"width","exact":"116","lowered":"116","lower":"116","upper":"116","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size y","role":"height","exact":"46","lowered":"46","lower":"46","upper":"46","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Path stroke width","role":"width","exact":"2","lowered":"2","lower":"2","upper":"2","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"90","lowered":"90","lower":"90","upper":"90","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"238","lowered":"238","lower":"238","upper":"238","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"18","lowered":"18","lower":"18","upper":"18","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"510","lowered":"510","lower":"510","upper":"510","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"200","lowered":"200","lower":"200","upper":"200","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"12","lowered":"12","lower":"12","upper":"12","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin x","role":"x","exact":"452","lowered":"452","lower":"452","upper":"452","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin y","role":"y","exact":"209","lowered":"209","lower":"209","upper":"209","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size x","role":"width","exact":"116","lowered":"116","lower":"116","upper":"116","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size y","role":"height","exact":"46","lowered":"46","lower":"46","upper":"46","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Path stroke width","role":"width","exact":"2","lowered":"2","lower":"2","upper":"2","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"510","lowered":"510","lower":"510","upper":"510","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"238","lowered":"238","lower":"238","upper":"238","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"18","lowered":"18","lower":"18","upper":"18","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"300","lowered":"300","lower":"300","upper":"300","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"328","lowered":"328","lower":"328","upper":"328","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"12","lowered":"12","lower":"12","upper":"12","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin x","role":"x","exact":"170","lowered":"170","lower":"170","upper":"170","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle origin y","role":"y","exact":"338","lowered":"338","lower":"338","upper":"338","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size x","role":"width","exact":"260","lowered":"260","lower":"260","upper":"260","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Rectangle size y","role":"height","exact":"48","lowered":"48","lower":"48","upper":"48","approximated":false,"certified":true,"error":0,"gain":1},{"path":"Path stroke width","role":"width","exact":"2","lowered":"2","lower":"2","upper":"2","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position x","role":"x","exact":"300","lowered":"300","lower":"300","upper":"300","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark position y","role":"y","exact":"368","lowered":"368","lower":"368","upper":"368","approximated":false,"certified":true,"error":0,"gain":1},{"path":"TextMark size","role":"font-size","exact":"16","lowered":"16","lower":"16","upper":"16","approximated":false,"certified":true,"error":0,"gain":1}],"collisions":[]}CURRENT0LEFT CHILD-1RIGHT CHILD1FORMULA RESULTx^2 = 0Choose a highlighted scene node to navigate.
Text alternative: Mathematical graphic

Mathematical graphic. 20 retained scene objects. 0 unresolved regions.

Coordinate rounding and uncertainty

Coordinates use nearest rounding at 6 decimal places. 0 numeric values were approximated; 0 distinct-value collision sets. Exact geometry uses outward enclosure with radius 0 SVG user units; this guarantee does not certify approximate inputs. No explicit clip regions; SVG overflow remains visible.

Exact sources and displayed SVG coordinates
CoordinateSourceDisplayedOutward boundsStatus and order
Graphic size 1600600600 to 600exact-number
Graphic size 2400400400 to 400exact-number
Path point 1 x300300300 to 300exact-number
Path point 1 y106106106 to 106exact-number
Path point 2 x909090 to 90exact-number
Path point 2 y208208208 to 208exact-number
Path stroke width333 to 3exact-number
Path point 1 x300300300 to 300exact-number
Path point 1 y106106106 to 106exact-number
Path point 2 x510510510 to 510exact-number
Path point 2 y208208208 to 208exact-number
Path stroke width333 to 3exact-number
TextMark position x300300300 to 300exact-number
TextMark position y505050 to 50exact-number
TextMark size121212 to 12exact-number
Rectangle origin x242242242 to 242exact-number
Rectangle origin y595959 to 59exact-number
Rectangle size x116116116 to 116exact-number
Rectangle size y464646 to 46exact-number
Path stroke width222 to 2exact-number
TextMark position x300300300 to 300exact-number
TextMark position y888888 to 88exact-number
TextMark size181818 to 18exact-number
TextMark position x909090 to 90exact-number
TextMark position y200200200 to 200exact-number
TextMark size121212 to 12exact-number
Rectangle origin x323232 to 32exact-number
Rectangle origin y209209209 to 209exact-number
Rectangle size x116116116 to 116exact-number
Rectangle size y464646 to 46exact-number
Path stroke width222 to 2exact-number
TextMark position x909090 to 90exact-number
TextMark position y238238238 to 238exact-number
TextMark size181818 to 18exact-number
TextMark position x510510510 to 510exact-number
TextMark position y200200200 to 200exact-number
TextMark size121212 to 12exact-number
Rectangle origin x452452452 to 452exact-number
Rectangle origin y209209209 to 209exact-number
Rectangle size x116116116 to 116exact-number
Rectangle size y464646 to 46exact-number
Path stroke width222 to 2exact-number
TextMark position x510510510 to 510exact-number
TextMark position y238238238 to 238exact-number
TextMark size181818 to 18exact-number
TextMark position x300300300 to 300exact-number
TextMark position y328328328 to 328exact-number
TextMark size121212 to 12exact-number
Rectangle origin x170170170 to 170exact-number
Rectangle origin y338338338 to 338exact-number
Rectangle size x260260260 to 260exact-number
Rectangle size y484848 to 48exact-number
Path stroke width222 to 2exact-number
TextMark position x300300300 to 300exact-number
TextMark position y368368368 to 368exact-number
TextMark size161616 to 16exact-number
20 semantic objects
  1. path: Path with 2 retained points
  2. path: Path with 2 retained points
  3. group: group containing 3 objects
  4. text mark: Text CURRENT at (300, 50)
  5. rectangle: Rectangle at (242, 59), size (116, 46)
  6. text mark: Text 0 at (300, 88)
  7. Go to left child: Go to left child, action scene-left
  8. group: group containing 3 objects
  9. text mark: Text LEFT CHILD at (90, 200)
  10. rectangle: Rectangle at (32, 209), size (116, 46)
  11. text mark: Text -1 at (90, 238)
  12. Go to right child: Go to right child, action scene-right
  13. group: group containing 3 objects
  14. text mark: Text RIGHT CHILD at (510, 200)
  15. rectangle: Rectangle at (452, 209), size (116, 46)
  16. text mark: Text 1 at (510, 238)
  17. group: group containing 3 objects
  18. text mark: Text FORMULA RESULT at (300, 328)
  19. rectangle: Rectangle at (170, 338), size (260, 48)
  20. text mark: Text x^2 = 0 at (300, 368)
Parent, current node, exact children, and the live formula result.

Exact node data

QuantityExact value
Current0
Depth0
Path[]
Farey boundaries( -1/0, 1/0 )
Continued fraction[0]
Convergents[0]
Formulax^2
Formula result0

Portable visible-tree records

These renderer-neutral records are the exact model that a richer browser tree layout can consume.

RoleRelative levelFractionParent
current00
descendant1-10
descendant110
descendant2-2-1
descendant2-1/2-1
descendant21/21
descendant221