Solved problems · 11 problems
Area & partitioning
Areas by coordinates and by DMD, curved boundaries, and the partition problems that split a parcel to a required area by a line of given direction or through a given point.
- Area of a closed parcel from coordinates by the shoelace ruleA five-corner parcel is given as plane coordinates. Work the cross-product sum term by term to square feet and acres, and use the sign of the result to prove the corner list is in boundary order.
- The same parcel by double meridian distanceThe HAWTHORN TRACT area recomputed on a DMD sheet — the form a plat's computation panel still shows — and set against the coordinate answer to prove the two methods are the same computation.
- Area of a parcel with one circular-arc boundaryA five-sided parcel whose southerly boundary is a circular arc. Compute the area of the chord polygon by coordinates, add the circular segment R²/2·(Δ − sin Δ), and check the segment as sector minus triangle.
- Area from a metes-and-bounds descriptionA deed of five calls reduced to latitudes and departures, carried to coordinates, and closed out to an area — with the description's own closure tested before the area is trusted.
- Partitioning a parcel by a cut line of given directionThree acres are to be severed from an eight-acre tract by a line parallel to the frontage. Set up the cut area as a quadratic in the perpendicular offset, solve it, and stake the two new corners.
- Partitioning a parcel by a line through a fixed pointA cut line must start at an existing monument on the frontage and sever 2.400 acres. Swing a trial line to a corner, then rotate it off that corner by the triangle the deficiency demands.
- Irregular boundary area by the trapezoidal rule and by Simpson's one-third ruleNine offsets to a meandering creek bank at 25 ft intervals, reduced two ways. The two rules differ by 22.5 ft², and the reason they differ is the reason to prefer one of them.
- Area of a PLSS aliquot part reconciled against a measured traverseThe nominal forty of a quarter-quarter set against the area its aliquot corners actually enclose. Build the aliquot corners by proportion from measured section corners, then compute what the description really conveys.
- Converting a computed area between square feet, acres and hectaresOne parcel area expressed in every unit a plat may call for, and the 4 ppm consequence of the two American feet made explicit — because 2 ppm in a length is 4 ppm in an area.
- Area of a right-of-way strip take along an alignmentA road widening takes a fifteen-foot strip along a frontage that runs partly on tangent and partly around a curve. The tangent part is a rectangle; the curved part is the difference of two circular sectors.
- Parcel area from a compass-rule-adjusted traverseField bearings and distances taken all the way through: closure, compass-rule adjustment, coordinates, and the area those adjusted coordinates enclose — with the adjustment's effect on the acreage measured rather than assumed.
Other categories
All problems- Curve stakingHorizontal and vertical curves solved from plan data and taken all the way to the stakes: stations, deflection angles, chords, offsets and grade elevations.
- Traverse adjustmentClosed traverses computed from field notes: angular closure, azimuths, latitudes and departures, misclosure and precision, compass-rule adjustment, final coordinates.
- Error propagationRandom error carried through sums, series, products and functions; weights and weighted means; the precision a procedure can actually deliver.
- Levelling loopsDifferential and trigonometric levelling reduced from notes, loop closure against a tolerance, and distribution of the misclosure.
- Boundary retracementGeneric retracement computations: proportionate measurement, aliquot subdivision of a section, and reconciling record and measured dimensions.