# Geometry Through Art

### Words

#### Space Words

top / bottom
front / back
near / far
left side / right side
inside / outside
in front of / behind
next to or beside
above / below
to the right / to the left
location or locus (a point)
POSITION, DIRECTION
compass directions: north, northwest, northeast; south, southwest, southeast; east, west
GEOMETRIC FIELD / PERCEPTUAL - VISUAL FIELD

#### Time/Motion Words

directions (motion): straight up / down - VERTICAL, sidewise - HORIZONTAL, slanting (uphill / downhill) - DIAGONALS
backward / forward (straight line) / spinning at a point - ROTATION
roll or slide / flip / turn
fast / slow
now / later
before / after
hour, half hour, quarter hour, minute, second
MAP COORDINATES

#### Measurement Words

similar, congruent
units of measure: inch, meter, mile, kilometer
percentage, degree
square units of measurement, perimeter, area
polygon numbers: square and rectangle numbers, triangle numbers, HEXAGON NUMBERS
whole / cardinal numbers
number line (left to add, right to subtract)
zero (as a point on a number line)
positive / negative numbers
odd / even numbers
commensurate / non-commensurate numbers
congruence
RATIO
PROPORTION
SCALE
RATE (of SPEED, i.e., DISTANCE x TIME)
whole / part
PI

#### Geometry/Art Words

Art/Design Words: Elements of design: dot, line, shape, direction, movement
color, tone, texture, pattern, dimension, scale

Principles of design: unity, variety, balance, emphasis, rhythm

STRUCTURE: RIGID / FLEXIBLE

Point Words: locus, intersect, vertex
Line Words: straight line, arc, line segment, ray
Polygon Words: triangle, square, pentagon, hexagon, HEPTAGON, octagon, NONAGON, decagon, dodecagon, ICOSAGON, regular polygon, rhombus, parallelogram, FACE (PLANE)
angle / side (contour or edge) / perpendicular / bisector / altitude / median

Circle Words: center / radius / circumference / diameter / sector / chord / CENTRAL ANGLE / INSCRIBED ANGLE / TANGENT, SUM OF ANGLE (360) DEGREES

Triangle Words: base, hypotenuse, altitude, median, Pythagorean theorem
Kinds of triangles: Pythagorean, right, isosceles, scalene, equilateral, obtuse, acute

Polyhedron Words: sphere, cube, cone, cylinder, prism 5 Platonic solids: tetrahedron, octahedron, cube, dodecahedron, icosahedron

Pattern Words: TESSELLATION, Unit of repeat (motif), transformations: slide, flip, rotate; symmetry, axis

Directional Words: vertical / horizontal, diagonal, rotational

Polygonal Numbers
PASCAL'S TRIANGLE
FIBONACCI NUMBERS

Kinds of geometry: plane geometry, solid geometry

### History of Geometry

Euclid's Elements
Thales
Pythagoras
Apollonius
Eudoxus
Great mathematicians from the school at Alexandria:
. . . Eratosthenes, Archimedes, Hipparchus

Leonardo DaVinci
Albrecht Durer
Nicholaus Copernicus
Johannes Kepler
Girard Desargues
Rene Descartes
Pierre Fermat
Leonhard Euler
John Bolyai

### 'Levels of Learning' Words

HEURISTIC (learning by finding out)

Van Hiele levels of learning geometry:

Level 0: PERCEPTION - VISUALIZATION
Level 1: ANALYSIS
Level 2: INFORMAL LOGIC
Level 3: FORMAL DEDUCTION
Level 4: RIGOR

### Materials

barbecue sticks and/or toothpicks
line and dot grid worksheets, square and triangular
polyhedral network worksheets printed on tagboard or sturdier paper more suitable for cutting, folding, and constructing 3-D constructions
percentage circle worksheets
poker chips
straight edge
scissors
Elmer's Glue
clear plastic disc (coffee can cover)
crayons or colored markers
plywood board and nails or cardboard for sewing string art designs