FS FLASHCARDS

A vocabulary deck summarizing fundamental formulas, surveying principles, GIS concepts, legal standards, and professional ethics from the lecture notes.

Distance Formula

√[(x₂ − x₁)² + (y₂ − y₁)²] gives the straight-line distance between two coordinate points.

Midpoint Formula

((x₁ + x₂)/2 , (y₁ + y₂)/2) finds the point halfway between two coordinates.

Slope Formula

m = (y₂ − y₁)/(x₂ − x₁) expresses the steepness of a line through two points.

General Form of a Line

Ax + By + C = 0 represents any straight line in Cartesian coordinates.

Point-to-Line Distance Formula

|Ax₀ + By₀ + C| / √(A² + B²) gives the perpendicular distance from point (x₀,y₀) to line Ax + By + C = 0.

Triangle Area (Sine Rule)

A = ½ab sin C when two sides a, b and included angle C are known.

Heron’s Formula

A = √[s(s − a)(s − b)(s − c)], where s = (a + b + c)/2.

Area of a Circle

A = πr² — the region enclosed by a circle of radius r.

Volume of a Cone

V = (1/3)πr²h — space inside a cone with base radius r and height h.

Angle Sum of a Triangle

The interior angles of any triangle add to 180°.

Law of Sines

sin A / a = sin B / b = sin C / c, relating sides and opposite angles in any triangle.

Law of Cosines

c² = a² + b² − 2ab cos C, generalizes Pythagoras for any triangle.

sin 30°

0.5

cos 60°

0.5

tan 45°

1

Sample Mean (x̄)

x̄ = (Σxᵢ)/n — average of a data set.

Sample Standard Deviation (s)

s = √[Σ(xᵢ − x̄)² / (n − 1)] measures spread of sample data.

Variance

The square of the standard deviation; quantifies data dispersion.

Normal Distribution

A bell-shaped, symmetric probability curve centered on the mean.

z-Score

Number of standard deviations a value lies from the mean.

Significant-Figure Multiplication Rule

Round final answer to the least number of sig figs in any factor.

Significant-Figure Addition Rule

Round result to the least number of decimal places among addends.

Determinant of a 2×2 Matrix

For [[a b],[c d]], det = ad − bc.

Matrix Inverse Method

Use A⁻¹ · b to solve linear systems Ax = b.

Identity Matrix

Square matrix with 1’s on the diagonal and 0’s elsewhere (acts like 1 in multiplication).

Matrix Multiplication (Transformations)

Represents combined rotations, scalings, and translations of coordinate geometry.

Power Rule (Derivative)

d/dx (xⁿ) = n xⁿ⁻¹.

Power Rule (Integral)

∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1.

Derivative – Physical Meaning

Instantaneous rate of change or slope at a point on a curve.

Integral – Physical Meaning

Accumulated quantity or area under a curve.

Derivative of sin x

cos x

Absolute Error

|Measured value − True value|.

Relative Error

Absolute error / True value (often expressed as a percentage).

Error Propagation (Addition)

Sum absolute errors when quantities are added or subtracted.

Error Propagation (Multiplication)

Add relative errors when quantities are multiplied or divided.

Engineer’s Scale 1″ = 50′

One inch on the drawing equals 50 feet on the ground.

Converting 1:24 000 Scale

1 inch on map equals 2 000 feet in reality.

Architect’s Scale ¼″ = 1′-0″

Every ¼ inch represents 1 foot at full size.

Graphic (Bar) Scale

Visual scale allowing distance measurement after plan enlargement or reduction.

Matchline

Indicates where one plan sheet continues onto another.

Title Block

Contains project name, sheet title, date, author, scale and drawing number.

Callout Reference

A code like “D5/S2” means Detail 5 on Sheet 2.

Northing & Easting

Grid coordinates: northing on Y-axis, easting on X-axis.

Slope Direction from Contours

Water flows downhill perpendicular to contour lines.

Hilltop (Contour Map)

Concentric closed contours with increasing elevation toward the center.

Contour Interval

Vertical elevation difference between successive contour lines.

Depression (Contours with Hachures)

Closed contours with short tick marks indicate a sink or depression.

Dashed Line (Site Plan)

Usually denotes a proposed or underground feature.

Benchmark Symbol

Triangle or “BM” with elevation value marks a known control point.

TYP

Abbreviation for “Typical” – condition applies wherever identical.

Iron Pipe Symbol

Circle with cross or “IP” label indicating a found iron pipe.

Elevation Axis on Profiles

Plotted on the vertical (Y) axis.

Horizontal Exaggeration (Profile)

Scales horizontal distances differently to highlight subtle elevation changes.

Road Cross-Section

Shows layers, slopes, and cut/fill from roadway centerline outward.

Point of Beginning (POB)

Starting point of a metes-and-bounds land description.

Metes & Bounds Units

Described in feet and degrees (e.g., N45°W 125.00′).

Plat

Recorded map showing lots, easements and property boundaries.

Bearing to Azimuth Conversion

Example: S45°E equals 135° azimuth clockwise from north.

NTS

Not To Scale (drawing not plotted at stated scale).

RCP

Reinforced Concrete Pipe.

FFE

Finished Floor Elevation.

CL

Centerline of a feature or alignment.

Geodetic Datum

Reference system defining Earth size, shape and coordinate origin/orientation.

NAD27 vs NAD83

NAD27 uses Clarke 1866 ellipsoid fixed in Kansas; NAD83 uses GRS80, Earth-centered.

WGS84

World Geodetic System 1984; global datum used by GPS.

Geoid vs Ellipsoid

Geoid follows mean sea-level gravity surface; ellipsoid is smooth mathematical model.

Modern U.S. Horizontal Datum

NAD83 (or NAD83 (2011) adjustment).

Local Datum

Reference system optimized for a specific geographic region.

Geographic Coordinate System

Positions by latitude and longitude on a sphere/ellipsoid.

Cartesian Coordinate System

X, Y, Z coordinates on a flat or rectified grid.

State Plane Coordinate System (SPCS)

Divides U.S. into low-distortion zones for surveying and mapping.

SPCS Units

Usually U.S. Survey Feet or International Feet depending on state.

Lambert Conformal Conic

Projection SPCS uses for east-west oriented zones.

Transverse Mercator (SPCS)

Projection SPCS uses for north-south oriented zones.

UTM Zone

6-degree longitude band in Universal Transverse Mercator grid.

Orthometric Height

Elevation above geoid (mean sea level).

Ellipsoidal Height

Height above the reference ellipsoid.

Height Relationship

Ellipsoidal = Orthometric + Geoid height.

NAVD88

North American Vertical Datum 1988 for U.S. elevations.

Geoid Height

Separation between ellipsoid and geoid at a location.

Map Projection

Method of representing Earth’s curved surface on a flat map.

Conformal Projection

Minimizes shape distortion (angles preserved).

Equal-Area Projection

Preserves area at the expense of shape or distance.

Common Survey Conformal Projection

Transverse Mercator.

Projection Drawback

All projections introduce distortion of area, shape, distance or direction.

GPS

Global Positioning System – U.S. satellite navigation network.

Satellites for 3-D Fix

Minimum of four.

Civil GPS Frequencies

L1 (1575.42 MHz) and L2 (1227.60 MHz).

Differential GPS (DGPS)

Uses base station corrections to improve positional accuracy.

Multipath Error

GPS signal reflected off surfaces, causing position inaccuracy.

PDOP

Position Dilution of Precision; lower values mean better satellite geometry.

Typical Civil GPS Accuracy

≈3–10 m uncorrected; sub-meter to centimeter with RTK.

RTK GPS

Real-Time Kinematic uses carrier phase for centimeter-level precision.

Reference Frame

Coordinate system plus time models defining positions (e.g., ITRF).

ITRF

International Terrestrial Reference Frame – global Earth-centered frame.

Coordinate Transformation

Converts positions between different datums or systems.

Transformation Types

Translation, rotation and scale change.

7-Parameter Transformation

Three shifts, three rotations, one scale factor.

Traverse

Series of linked survey lines with measured lengths and directions.

Open vs Closed Traverse

Open ends at unknown point; closed returns to start or known point.