This Glossary is produced to help promote consistency in the usage of words and terms that are common to math trails of different types. 

2-DIMENSIONAL: relating to an object with length and width on a plane.

3-DIMENSIONAL: relating to an object with width, length and height in space.  

ABSTRACT: a style of art that is not realistic, containing geometric and organic shapes.

ACUTE: an angle that is less than 90 degrees.

AESTHETIC: concerned with beauty; a set of principles or approach to the visual qualities of an object

ALGEBRA: the branch of mathematics in which letters and other symbols are used to represent numbers, values and quantities to state relations.

ANGLE: a space (measured in degrees) formed by the intersection of 2 rays, lines or surfaces.

ARC: a segment of a circle or curve.

ARCADE: a series of arches supported by columns or piers that may be attached to a wall or freestanding. 

ARCH: a method of spanning an opening; usually a curved or pointed structural member.

ARCHIMEDEAN SOLIDS: 13 semi-regular convex polyhedra, comprised of regular polygonal faces that surround every vertex in the same sequence.

ARCHITECTURE: relating to the design and construction of buildings and other physical structures.

AREA: the quantity of space inside a two dimensional figure.

ASYMMETRIC: absence of parts that are not the same in shape, size and arrangement.

AXIS: the perpendicular lines of a coordinate system; the central line around which something rotates or reflects.

BALANCE:  the equalization of the elements in a work of art or architecture, element of nature, or equation. 

BALUSTRADE: a railing of small posts topped by a cap at the edge of stairs or on a roof. 

BARRIER: a design and construction term referring to fences, stone walls, retaining walls, guard rails, etc.

BILATERAL: affecting both sides; symmetrical halves.

BIODIVERSITY: The variety of plant and animal life in a habitat or ecosystem.

BIOMORPHIC: patterns or shapes resembling nature and living organisms.

BISECT: cut into two congruent halves.

BRIDGE: a structure carrying a road, path, walkway, or railroad that is built over a river, road, railroad, or other obstacle to enable crossing from one side to another.

BUTTRESS: a projecting mass, typically of brickwork or masonry, that is used to support a structure.

CANTILEVER: a beam or other or other structural projection that projects beyond its supporting wall or column.

CANON: a general principle or rule by which something is evaluated.

CAPITAL: the top part of a column or pillar.

CENTRAL ANGLE: an angle in a circle with a vertex at the circle's center point.

CHIRAL: asymmetric such that the object cannot be superimposed on its mirror image.

CHORD: a line segment across the interior of a circle whose endpoints are on the circle.

CIRCLE: the set of all points that are equidistant from a center point.

CIRCUMFERENCE: the distance around the outside of a circle. 

CIRCUMSCRIBE: to surround by a circle.

CLOCKWISE: the forward directional movement of the hands of a clock.

COLLINEAR: lying on the same line.

COMPLEMENTARY: the sum of angles equal to 90 degrees; elements not contained in a given set; the opposite of an event.

COMPOSITION: the way in which elements of a whole are configured.

CONCAVE: a shape or solid that has an indentation (caves in).

CONCENTRIC: similar figures or shapes that share a common center.

CONE: a 3-dimensional figure or shape with a round base that tapers to a vertex.

CONGRUENT: exactly the same size and shape.

CONTRACTION: a transformation in which a figure grows smaller; all distances are shortened by a common factor.

CONVEX: an outline or surface of a figure that has no indentations.

COORDINATES: the numbers giving the location of a point in a 2 or 3-dimensional system.

CORNICE: A molding or ornamentation that projects from the top of a building.

CRESCENT: a curved sickle shape that is broad in the center and tapers to a point at each end.

CRYSTAL: a solid, whose elements are arranged in a defined pattern and surface regularity reflects its internal symmetry.

CUBE: a 3-dimensional object with 6 congruent square sides.

CUPOLA: a small structure situated on top of a roof, often domed with solid walls or four arches, which covers a circular or polygonal area. 

CURVE: any path, curved or straight and open or closed on a plane or in a 3-dimensional space.

CYLINDER: a 3-dimensional solid with parallel and congruent circular bases.

DECAGON: a figure on a plane, a polygon, with 10 straight sides.

DEGREE: a unit of angle measure equal to a complete revolution; 360 degrees in a circle.

DESCRIPTIVE GEOMETRY: branch of mathematics used to transform 3-dimensional objects into 2-dimensional representations.

DIAGONAL: a line segment connecting non-adjacent corners of a polygon or space.

DIAMETER: A line segment between two points on a circle or sphere that passes through the center. 

DIHEDRAL ANGLE: An angle formed by intersecting planes.

DILATION: a transformation in which a figure grows larger, proportionally at every point.

DIMENSION: measurements describing the size of an object or space, typically referring to length, width and height.

DODECAHEDRON: a polyhedron with 12 faces; a regular polyhedron is one of the Platonic solids.

DOME: a rounded vault, usually a cross-section of a sphere or ellipse.

ECOLOGY: the study of interactions among organisms and their environment.

ECOSYSTEM: a community or system of interacting organisms and their physical environment.

EDGE: a line segment on a polyhedron, where two faces intersect.

ELLIPSE: a curve in a plane, an oval shape, a stretched circle, which is a planar section of a cone.

EQUILATERAL: all sides are congruent.

EQUIDISTANT: equal distantances from a point and each object in the set. 

EXPLEMENTARY: angles whose sum is 360 degrees.

EXPONENT: the number of times a number is multiplied by itself, which appears as a superscript to a number when written.

FAÇADE: The exterior face of a building, which is the architectural front

FORM: the shape and structure of something.

GEOMETRIC ABSTRACTION: non-representational art using simple geometric forms and focusing on primary colors, flatness, grids and patterns.

GEOMETRIC MODELING: relating to the construction of free-form curves, surfaces, or volumes in architectural design.

GLIDE (REFLECTION): a transformation in which a graph or figure is moved to another location on a grid without any change in size or orientation.

GOLDEN RATIO: a number with a value approximating 1.61803, which refers to 2 quantities whose relationship is the same as the relationship of their sum to the larger of the 2 quantities.

GRAPH: the image formed by plotting points on a number line, coordinate plane or 3-dimensional coordinate system.

FACE: one of the flat (polygonal) surfaces that make up a polyhedron.

FIBONACCI NUMBERS: the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . in which each subsequent term is found by adding the previous two terms. The ratio of successive numbers approximate the Golden Ratio at its limit.

FLORA: the plants of a particular region, habitat, or geological period.

FOCAL POINT: the area in a composition where the emphasis is greatest. 

FRACTAL:  a figure that is self-similar; each part has the same pattern as the whole. 

GEOMETRY: the study of figures in 2 and 3 dimensions, which includes points, lines, polygons, circles, spheres, prisms, pyramids, cones, cylinders and polyhedra. 

GREENWAY: a corridor of undeveloped land that has been preserved for recreational use or environmental protection.

GRID: a framework of uniformly spaced bars that are parallel and perpendicular to one another.

HABITAT: the natural home or environment in which an organism lives.

HELIX: a curve shaped like a spring. 

HORIZONTAL: flat and level, parallel to the plane of the horizon.

HYPERBOLA: a symmetrical curve, formed by planar section of a cone, that some view as an inside-out ellipse.

IMPOSSIBLE CONSTRUCTIONS: (informal) type of optical illusion where space and planes coexist and distorted representations obliterate distinctions between up and down or background and foreground.

INFINITY: a quantity, size, or magnitude that is larger than any real number.

INSCRIBE: to draw a shape within another with touching but non-intersecting boundaries.

INTERSECT: where lines, planes or solids cross; common elements of elements two or more sets.

KEYSTONE: The central wedge-shaped stone at the crown of an arch that supports it.

KINETIC: including motion or movement.

KITE: a 4-sided polygon with 2 sets of adjacent congruent sides.

LATTICE: an interlaced structure, with repeating arrangement of points or lines.

LINE: the straight path of a moving point, which is infinite in length.
Linear perspective:

LINTEL: a horizontal structure like a beam that spans an opening for support.

LOCUS: a set of points that forms a geometric figure or graph.

LUCAS NUMBERS: a numbers series beginning with 2, 1, 3, 4, 7, 11, 18... that like the Fibonacci numbers are formed by adding the latest two values. The ratios of successive numbers approximate the Golden Ratio at its limit.

MATH TRAIL: a tour of an environment for the discovery of examples of math concepts, including measurement, symmetry, data analysis and probability, patterns, graphing, algebra, and geometry; and math processes including problem solving, communication, reasoning, connections and representations.

MEASUREMENT: the system of units and process of assigning a number to a physical property.

MOBILE: a hanging sculpture that has elements that move freely.

MOBIUS STRIP: a one-sided (edged) surface formed by joining two ends with a half-turn in the middle.

MOTIF: a pattern, design or unit that is repeated to create visual rhythm or convey importance or a theme.

NEGATIVE SPACE: the space around and between the elements of an image.

OBELISK: a stone pillar, typically with a rectangular cross section and pyramidal top.

OCTAGON: an 8-sided polygon.

ORDER OF SYMMETRY:  is the number of times a figure coincides with itself as its rotates through 360 degrees.

ORGANISM: something having many related parts that function together as a whole; any living plant, animal or other life form.  

PALINDROME: a word or sequence of symbols, numbers or elements that reads the same forward or backward.

PARABOLA: a plane curve, which is symmetrical and approximately U-shaped, that is a graph of a quadratic function.

PARALLEL: distinct coplanar lines that do not intersect, hence are equidistant from one another at every set of corresponding points. 

PARALLELOGRAM: A quadrilateral with 2 pairs of parallel sides.

PATTERN: a repeated design, or set of elements that repeat in a predictable or defined manner.

PENTAGON: a five-sided polygon.

PERIMETER: the distance around the outside of a polygon or plane figure. 

PERPENDICULAR: lines, planes or surfaces that meet at 90 degree angles.

PERSPECTIVE: The illusion of a 3-dimensional space on a 2-dimensional plane through the use of vanishing point and converging lines, in which diminishing sizes suggest depth.

PLANE: a flat surface extending in all directions. 

PLANE TILING: a tessellation of a flat surface, which uses one or more geometric shapes (tiles), with no overlaps or gaps. 

PLATONIC SOLIDS: the 5 solids that have faces that are all congruent regular polygons.

POINT: an exact position or place on a plane surface.

POLYGON: a closed plane figure in which all sides are line segments. 

POLYHEDRON: A solid with flat surfaces and edges in which all faces are polygons and all edges are line segments.

PORTICO: an open porch with columns supporting a roof, creating the entrance or centerpiece of a facade. 

PRIME: A number only divisible by itself and 1.

PRISM: a solid with parallel congruent bases that are both polygons and rectangular lateral faces.

PROBABILITY: the branch of mathematics that quantifies the likelihood of an event occurring. 

PROJECTIVE PLANE: a plane equipped with additional "points at infinity" where parallel lines intersect. 

PROPORTION: two equivalent ratios. 

PYRAMID: a polyhedron with a polygonal base and triangular lateral faces that taper to an apex.

PYTHAGOREAN THEOREM: an equation relating the lengths of the sides of a right triangle, in which the he sum of the squares of the legs is equal to the square of the hypotenuse.

QUADRILATERAL: a four-sided polygon.

RADIUS: the distance from the center of a circle to any point on its circumference.

RATIO: the quantitative relationship between 2 amounts. 

RECTANGLE: a 4-sided polygon with 4 right, hence congruent, angles. 

REFLECTION: a transformation in which a geometric figure is reflected across a line, creating a mirror image.

REFRACTION: the bending of light as it passes from one transparent substance to another .

RHOMBUS: a parallelogram with 4 congruent sides. 

ROTATION: a transformation in which a plane figure moves in a circle around a fixed center point.

ROTATIONAL SYMMETRY: a shape that looks the same (coincides with itself) after it moves around a fixed center point in less than a full turn (at an angle between 0 and 360 degrees). 

ROTUNDA: A circular room, often with a dome.

SCALE DRAWING: A drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale) and therefore all dimensions are proportionate to the actual object.

SCULPTURE: a 3-dimensional work of art.

SECTION: A 2 dimensional drawing of a building sliced through. The section is usually an interior elevation of part of the building.

SELF-SIMILARITY: a property of fractals in which the pattern of the whole occurs in each part.

SHAPE: the external form of something.

SLOPE: is a measure of the steepness of a line, defined as the ratio of rise over run

SPHERE: a 3- dimensional solid in which all points are equidistant from the center point. 

SPIRAL: a curve on a plane that turns endlessly outward and/or inward.

SQUARE: a quadrilateral with 4-congruent sides and 4-90 degree angles.

STEINER SURFACE: or Roman surface is an image of the projective plane and one of the 3 possible surfaces obtained by sewing a Möbius strip to the edge of a disk.

STEAM: an interdisciplinary curriculum comprised of 5 specific disciplines — science, technology, engineering, art and mathematics to guide student inquiry, dialogue, and critical thinking. 

STEM: an interdisciplinary curriculum comprised of 4 specific disciplines — science, technology, engineering and mathematics. 

SUPPLEMENTARY: a set of angles that add up to 180 degrees.

SURFACE AREA: the total area of the exterior surface of a solid.

SUSTAINABLE: avoidance of the depletion of natural resources through conservation and rejuvenation.

SYMBOL: a mark, character or letter used as a representation of an object, number, function, or process. 

SYMMETRY: when two or more parts are identical after a flip, slide or turn. 

TESSELLATION: covering a plane with geometric shapes in a repeating pattern that does not overlap or leave blank spaces.

TETRAHEDRON: a polyhedron with four triangular faces, a pyramid with a triangular base.

TORUS: a doughnut shape with no edges or vertices.

TOPOGRAPHY: arrangement of the natural and physical features of an area.

TRANSFORMATION: the movements of objects in a plane that alters the form of a figure including translations, reflections, dilations, compressions, and rotations.

TRANSLATION: a transformation in which a graph or geometric figure is relocated to another location without any change in size or orientation.

TRANSOM: the horizontal framing member between a door and a window above; also refers to the window above a door. 

TRAPEZOID: a quadrilateral with exactly one pair of opposite parallel sides. 

TRIANGLE: a polygon with 3 sides.

TRUNCATED: cut off or cut short, usually in reference to a roof.

VAULT: An arched structure of stone, brick or reinforced concrete forming a ceiling or roof over a wholly or partially enclosed 

VANTAGE POINT: a position or standpoint from which something is viewed.

VERTEX: a corner point of a geometric figure; a vertex on a polygon is where 2 adjacent sides meet; a vertex of an angle is where its 2 rays meet; a vertex of a polyhedron is where 3 edges meet.

VERTICAL: at right angles to a horizontal plane; having an alignment, such that the top is directly above the bottom.

VOLUME: the total amount of space enclosed in a solid.

WALLPAPER GROUP: a mathematical classification of the 17 distinct groups of 2-dimensional repetitive and symmetrical patterns.