**by Bill Lauritzen**

If Kids Could Vote

Geometry = Shapes

Plane Geometry = Flats

**Solid Geometry = Shapes**

plane figure | 3 | flat | 1 |

3-D figure or spacial figure | 4 | shape | 1 |

perimeter | 4 | around or border or fence | 2 |

area | 3 | skin or fill | 1 |

volume | 2 | fill | 1 |

Thus:

length of a line

skin of a flat

fill of a shape

Old: The area of a rectangle is length times width. To find the perimeter of a rectangle add the lengths of all the sides. The volume of a cube is length time width times height.

New: The skin of a rectangle is length times width. To fence a rectangle add the lengths of all the sides. The fill of a cube is length times width times height.

diameter | 4 | across | 2 |

radius | 3 | spoke | 1 |

circle | 1 | ring, wheel, roll, round, O (say “oh”) | 1 |

sphere | 1 | ball | 1 |

cylinder | 3 | can | 1 |

degrees | 2 | twiks | 1 |

ellipse | 2 | oval | 2 |

The Chinese use "straight-line" and "half-line" for diameter and radius.

ring = fat-ring

Old: The circumference of any circle divided by the diameter of the circle is the same: 3.14, or pi. A circle has 360 degrees. The volume of a cylinder equals pi times the radius squared times the height.

New: The around of any ring divided by the across of the ring is the same: 3.14, or pi. A ring has 360 twiks. The fill of a can evens pi times the spoke two’d times the height.

angle | 2 | nik | 1 |

measure of an angle | 6 | turn of a nik | 4 |

triangle | 3 | 3-nik or simplat | 1 |

vertex | 2 | nik-dot (2D) or nook-dot (3D) | 1 |

2-D | 2 | flat | 1 |

polygon | 3 | many-nik or n-nik | 3 |

parallel | 3 | along | 2 |

quadrilateral family = four-nik family

quadrilateral | 5 | 4-nik | 2 |

square | 1 | square or even 4-nik | 1 or |

trapezoid | 3 | track-4-nik | 4 |

parallelogram | 5 | all-track-4-nik | 3 |

rhombus | 2 | same-side-4-nik | 4 |

polygons = many-niks or n-niks or flats

pentagon | 3 | 5-nik | 2 |

hexagon | 3 | 6-nik | 2 |

decagon | 3 | 10-nik | 1 |

icosagon | 4 | 20-nik | 3 |

regular | 3 | even | 2 |

irregular | 4 | uneven | 1 |

regular pentagon | 6 | even 5-nik | 4 |

irregular pentagon | 7 | uneven 5-nik | 3 |

etc.

Old: The regular hexagon has 6 equal sides and six equal angles.

New: The even 6-nik has 6 matching sides and 6 matching niks.

ruler | 2 | straight-edge | 2 |

protractor | 3 | nik-ring | 2 |

compass | 2 | ring-maker | 3 |

chord | 1 | -- | 1 |

secant | 2 | ring-line | 2 |

secant segment | 4 | ring-linet | 3 |

exterior secant segment | 8 | out-ring-linet | 4 |

Old: Triangles are the only stable polygon. If one puts string through drinking straws, this is easy to demonstrate. A quadrilateral, hexagon, decagon, icosagon, in fact all other polyhedra, will collapse, while the triangle keeps its shape.

New: Three-niks are the only stable many-niks. If one puts string through drinking straws, this is easy to demonstrate. A 4-nik, 6-nik, 10-nik, 20-nik, in fact all other many-niks, will collapse, while the 3-nik keeps its shape

rectangle | 3 | right 4-nik | 3 |

rhombus | 2 | -- | 2 |

point | 1 | dot or point | 1 |

line | 1 | -- | 1 |

plane | 1 | flat or flat-go (infinite) | 3 |

ray | 1 | -- | 1 |

segment | 2 | seg or linet | 2 |

coplanar | 2 | same-flat | 2 |

collinear | 4 | same-line | 2 |

Old: The line crossed the plane at one point.

New: The line crossed the flat at one dot.

monomial | 4 | one-term | 2 |

binomial | 4 | two-term | 2 |

polynomial | 5 | many-terms | 3 |

Polyhedra = many-nooks or n-nooks

polyhedron | 4 | many-nook or | 3 |

face | 1 | flat | 1 |

edge | 1 | lip | 1 |

vertex | 2 | nook | 2 |

3-D | 2 | shape | 1 |

tetrahedron | 4 | 4-nook or simplex | 2 |

octahedron | 4 | 6-nook | 2 |

hexahedron | 4 | 8-nook | 2 |

cube | 1 | even-box or box | 1 |

icosahedron | 6 | 12-nook | 2 |

dodecahedron | 5 | 20-nook | 3 |

Nook is used because it is another name for a corner and the number of corners can identify the five elemental polyhedra.

Old: A tetrahedron has 4 vertices, 6 edges, and 4 sides.

New: A 4-nook has 4 nooks, 6 lips, and 4 flats.

Old: Sides + vertices – edges = 2

New: Flats + nooks – lips = 2

simplest flat figure = simplat = three-nik

simplest spacial shape = simplex = four-nook

regular tetrahedron | 7 | even 4-nook | 4 |

irregular tetrahedron | 8 | uneven 4-nook | 3 |

regular octahedron | 7 | even 6-nook | 5 |

irregular octahedron | 8 | uneven 6-nook | 3 |

regular hexahedron or cube | 7 | even-box or even 8-nook | 4 |

helix | 2 | coil | 1 |

conical helix | 5 | cone-coil | 2 |

spiral | 2 | -- | 2 |

conical sections | 5 | cone slices | 3 |

hyperbola | 4 | far-throw | 2 |

parabola | 4 | throw | 2 |

dihedral angle | 5 | two-flat nik | 3 |

prism = two-base-match-track

[The two bases of the shape match and track.]

Some Archimedean polyhedra:

cubeoctahedron | 5 | cubic-6-nook | 4 |

truncated tetrahedron | 7 | cut-off-4-nook | 4 |

pentagonal prism | 6 | 5-nik prism | 4 |

Old: There are only five regular polyhedra. Because they are made of triangles, tetrahedrons, octahedrons, and icosahedron are stable. Hexahedrons and dodecahedrons are not.

New: There are only 5 even many-nooks. Because they are made of 3-niks, 4-nooks, 6-nooks, and 20-nooks are stable. 8-nooks and 12-nooks are not.

scalene triangle | 5 | no-match 3-nik | 4 |

isosceles triangle | 7 | two-match three-nik | 4 |

equilateral triangle | 8 | even three-nik | 4 |

Old: The measures of the angles of a triangle always add up to 180 degrees. In an equilateral triangle, all the sides and angles are equal.

New: The measure of the niks of a 3-nik always adds up to 180 twiks. In an even 3-nik, all the sides and niks match.

right angle | 3 | right nik or fourth-nik | 2 |

right triangle | 4 | right 3-nik | 3 |

hypotenuse | 4 | long or shlong | 1 |

legs | 1 | -- | 1 |

opposite side | 4 | far side | 2 |

adjacent side | 4 | by side | 2 |

Old: A right triangle has two legs and a hypotenuse.

New: A right 3-nik has two legs and a shlong.

congruent | 3 | matching | 2 |

similar | 3 | zoom or zoomy | 1 |

["Similar triangles" can be called "zoom triangles" or "zoomies" because of the widespread use of the zoom lens, which was unknown to the ancients. Of course, one may have to flip and/or spin the triangle to see the "zoomability." Zoom here does refer to an actual increase in size not an illusory increase in size as in a lens.]

similar triangles | 6 | zoomy three-niks | 4 |

similar figures | 5 | zoomies | 2 |

similarity | 5 | zoomity | 3 |

scale factor | 3 | zoom factor | 3 |

proportion | 3 | zoom or to-to* | 2 |

* a is to b as c is to d.

proportional | 4 | zoomable or to-to | 2 |

direct | 2 | straight | 1 |

inverse | 2 | flip | 1 |

direct proportion | 5 | straight-zoom or boost | 1 |

inverse proportion | 5 | flip-zoom or shrink | 2 |

positive | 3 | front | 1 |

negative | 3 | back | 1 |

positive numbers | 5 | fronts | 1 |

negative numbers | 5 | backs | 1 |

opposite | 3 | back | 1 |

reciprocal | 4 | flip | 1 |

corresponding side | 5 | like-side | 2 |

Old: The corresponding sides of similar triangles are directly proportional.

New: The like sides of zoom 3-niks are zoomable.

The pull between masses boosts with an increase in mass and shrinks with an increase in distance.

acute angle | 4 | sharp nik | 2 |

obtuse angle | 4 | blunt nik or dull nik | 2 |

complementary angles | 7 | right-fill niks* | 3 |

complement | 3 | right-fill | 2 |

supplementary angles | 7 | straight-fill niks | 3 |

supplement | 3 | straight-fill | 2 |

-- | 3 | ring-fill niks | 3 |

* The two angles fill a right angle.

90 = right-fill

180 = straight-fill

360 = ring-fill

Old: An acute angle is less than 90 degrees. An angle and its complement add up to 90 degrees.

New: A sharp nik is less than 90 twiks. A nik and its right-fill add to 90 twiks.

perpendicular | 5 | right-crossing or right | 1 |

induction | 3 | making-a-rule | 4 |

deduction | 3 | using-a-rule | 4 |

bisector | 3 | halfer | 2 |

mid-point | 2 | half-point | 2 |

perpendicular bisector | 8 | right halfer | 3 |

interior | 4 | in | 1 |

exterior | 4 | out | 2 |

corresponding angles | 6 | kin-niks or like-niks | 2 |

adjacent angles | 5 | by-niks | 2 |

interior angle | 5 | in-nik | 2 |

exterior angle | 6 | out-nik | 2 |

vertical angles | 5 | facing niks | 3 |

transversal | 3 | crosser or cut | 1 |

consecutive interior angles | 8 | same-side in-niks | 4 |

consecutive exterior angles | 8 | same-side out-niks | 4 |

alternate interior angles | 9 | other-side in-niks | 4 |

alternate exterior angles | 9 | other-side out-niks | 4 |

tangent line | 3 | touching line or touch | 1 |

cone | 1 | -- | 1 |

arc | 1 | -- | 1 |

subtends | 2 | makes or forms | 1 |

convex | 2 | out | 1 |

convex polygon | 5 | out-many-nik | 4 |

concentric circles | 5 | same-center rings | 4 |

lateral | 3 | side | 1 |

lateral area | 6 | side fill or side skin | 2 |

inscribe | 2 | in-draw or in-fit | 1 |

circumscribe | 3 | around-draw or out-fit | 2 |

Old: If two parallel lines are crossed by a transversal, then each pair of alternate interior angles are congruent.

New: If two along lines are crossed, then each pair of other-side in-niks match.

Old: If two parallel lines are crossed by a transversal, then each pair of consecutive interior angles are supplementary.

New: If two along lines are crossed, then each pair of same-side in-niks straight-fill.

Old: If two parallel lines are crossed by a transversal, then each pair of alternate exterior angles are congruent.

New: If two along lines are crossed, then each pair of other-side out-niks match.

constant | 2 | still | 1 |

intersection | 4 | cross* or cut | 1 |

union | 2 | -- | 2 |

axis of symmetry | 6 | line of turn-same | 4 |

Venn diagram | 4 | overlap* | 3 |

cumulative amount | 6 | so-far-sum | 3 |

dimensions | 3 | measures (of a blueprint) | 2 |

consecutive | 4 | next-to | 2 |

conjunction | 3 | and-say | 2 |

disjunction | 3 | or-say | 2 |

symmetry | 3 | turn-same | 2 |

transformations | 4 | changes | 2 |

rotation | 3 | spin | 1 |

translation | 3 | slide | 1 |

shear | 1 | -- | 1 |

stretch | 1 | -- | 1 |

reflection | 3 | mirror | 1 |

center of rotation | 6 | spin point | 2 |

proof | 1 | showing | 2 |

prove | 1 | show | 1 |

conjecture | 3 | guess | 1 |