He rārangi kupu e pā ana ki tēnei peka o te wānanga pāngarau.
A vocabulary list relating to this area of mathematical understanding.
sine (tohu: sin)
chord (takenga mai: aho - weft, cross threads of weaving; aho - line, cord)
inverse sine (tohu: 
)
dimension (of space)
direction, bearing, orientation, directed toward (kupu kē atu: anga, aro ~nga)
two-dimensional (whakapotonga: ahu-2) (kupu kē atu: ahurua)
one-dimensional (whakapotonga: ahu-1)
three-dimensional (whakapotonga: ahu-3) (kupu kē atu: ahutoru)
shape (kupu kē atu: hanga)
āhua ahu-3 mata kōpiko Tūingoa
curved solid
āhua ahu-3 mata kōpiko, mata papatahi Tūingoa
solid with curved and flat surfaces
two-dimensional figure (whakapotonga: āhua ahu-2)
three-dimensional figure, solid (shape) (whakapotonga: āhua ahu-3)
curvilinear shape
geometry
transformation geometry
circle geometry
co-ordinate geometry
attribute, feature, property
invariant property (takenga mai: āhuatanga – property; pūmau – fixed, constant, permanent)
variant property (takenga mai: āhuatanga – property; taurangi – variable)
opposite direction, inverse direction
simple curve (kupu kē atu: kōpiko māmā)
simple open curve
simple closed curve
scale (takenga mai: arawhata – ladder)
perpendicular, at right angles (takenga mai: hāngai – across, at right angles, astride)
hangarite Tūingoa, Tūmahi Poro, Tūāhua
symmetrical, symmetry (takenga mai: hanga – shape; rite – alike, corresponding)
rotational symmetry
line symmetry, reflective symmetry
tangram (takenga mai: hanga – shape; whitu – seven)
diagonal
irregular, asymmetric (takenga mai: hikuwaru – crooked, asymmetrical)
hoahoa ~ina Tūingoa, Tūmahi Whiti
diagram (takenga mai: hoahoa – plan of a house)
floor plan
scale drawing, scale diagram
isometric diagram
area (takenga mai: hora – spread out)
surface area
oblique (takenga mai: hōtiu – oblique, inclined)
locus (takenga mai: huanui – path, pathway)
horizontal (kupu kē atu: pae, whakapae)
huri ~hia ~hanga Tūingoa, Tūmahi Whiti
rotate, rotation, turn
half-turn (180˚)
quarter-turn (90˚)
overlap
protractor
clinometer (takenga mai: ine – measure; rōnaki – sloping, slanting)
isometric (takenga mai: ine – measure; rite - alike, corresponding)
dot, point (takenga mai: ira – freckle, mole) (kupu kē atu: tongi)
compass (direction)
kauhuri ~a ~nga Tūingoa, Tūmahi Poro
flip (kupu kē atu: huripoki)
anticlockwise
cone, pyramid
right cone, right pyramid
oblique cone, oblique pyramid
hexagonal pyramid (regular)
triangular pyramid (regular), tetrahedron (kupu kē atu: matawhā [rite])
rectangular pyramid
square pyramid
koeko-tapawhā rite hōtiu Tūingoa
oblique square pyramid
distinctive, prominent (takenga mai: kōhure – outstanding, conspicuous) (kupu kē atu: tāpua)
angle
right angle (tohu: 
)
obtuse angle (takenga mai: koki – angle; hāpūpū – blunt)
whole angle, full turn (360˚)
tangential angle
adjacent angle
central angle
straight line angle (kupu kē atu: koki torotika)
inscribed angle
reflex angle
angle of elevation
interior angle, internal angle
acute angle (takenga mai: koki – angle; tāhapa – at an acute angle) (kupu kē atu: koki koi)
angle of depression
opposite angle
corresponding angle
co-interior angle
alternate angle
exterior angle, external angle
complementary angles (takenga mai: koki – angle; whaka – causative prefix, to make; hāngai – perpendicular)
conjugate angles (takenga mai: koki – angle; whaka – causative prefix, to make; huri – turn; pū – origin, heart, centre)
supplementary angles (takenga mai: koki – angle; whaka– causative prefix, to make; rārangi – line)
corner (kupu kē atu: akitu)
concave
curve, curved
open curve
closed curve
convex
kite shape (takenga mai: manu - kite; tapawhā – quadrilateral)
face (of a solid figure)
icosahedron (regular)
mata-tekau mā rua (rite) Tūingoa
dodecahedron (regular)
multilink cubes (kupu kē atu: poraka honohono, poro honohono)
cube (takenga mai: mata - face; ono - six; rite - similar, alike)
Soma cube
polycube
polyhedron (regular) (takenga mai: mata – face; rau –many; rite - alike, similar)
octahedron (regular) (takenga mai: mata - face; waru - eight; rite - similar, alike)
tetrahedron (regular) (takenga mai: mata - face; whā - four; rite - similar, alike) (kupu kē atu: koeko-tapatoru [rite])
helix (takenga mai: maurea - tiger shell)
space, spatial
cross-section (takenga mai: motu – severed, cut)
oblique cross-section
horizontal cross-section (kupu kē atu: motupae)
frustum (takenga mai: motu – severed, cut; pūtake – base)
systematic (takenga mai: nahanaha – well arranged, in good order)
equal, congruent (tohu: =)
similar (shape)
equivalent (size), same amount
answer, product, quotient, result, solution (takenga mai: oti – finished, completed) (kupu kē atu: hua)
ratio (tohu: :) (takenga mai: ō - of, belonging to; wehenga - portion, part, division)
golden ratio (takenga mai: ōwehenga - ratio; huatau - comely, suitable, elegant, graceful)
trigonometric ratio
tangential ratio
pi (tohu: π) (takenga mai: He kupu mino [reo Kiriki].)
circumference, perimeter
paenga (o te) porowhita haurua Tūingoa
semicircumference
trigonometry (takenga mai: pā – connected with; koki – angle)
puzzle, guessing game
panoni ~hia ~ tanga Tūingoa, Tūmahi Whiti
transform, transformation (takenga mai: panoni – change)
repeated transformation
tile (takenga mai: papa – anything broad, flat and hard; riki – small)
flat
parahau ~tia ~tanga Tūingoa, Tūmahi Whiti
justify, justification (takenga mai: parahau – protection, defence)
tangent (trigonometry) (tohu: tan)
tangent (to curve) (takenga mai: pā – connected with, touch; tapa – edge)
inverse tangent (tohu: 
)
adjacent
grid paper
arrow
chevron (kupu kē atu: kaokao)
arrow head shape
arc (takenga mai: pewa – anything bow-shaped)
minor arc
major arc
sector
minor sector
major sector
quatrefoil (takenga mai: pewa - arc, arched; whā - four)
hemisphere
ovoid (takenga mai: poi – sphere; hema – tapering)
ellipsoid (takenga mai: poi – sphere; rapa – spread out, extended)
prism (takenga mai: poro – butt end, block)
block (kupu kē atu: poraka)
attribute block
hexagonal prism
trapezoidal prism
pentagonal prism
triangular prism
octagonal prism
rectangular prism, cuboid
square prism
poro-tapawhā rite hōtiu Tūingoa
oblique square prism
oval (takenga mai: poro [porowhita] – circle; hema – tapering)
ellipse (takenga mai: poro [porowhita] – circle; rapa – spread out, extended)
porowhita ~tia Tūingoa, Tūmahi Whiti, Tūāhua
circle (kupu kē atu: porohita ~tia)
semicircle
quadrant
tangential circles
concentric circles
incircle, inscribed circle
circumcircle
vertical (kupu kē atu: pou, poupou)
incentre
circumcentre
centroid (of a triangle)
invariant, fixed, constant
concentric (takenga mai: pū – centre; rite – alike, corresponding)
pūtahi ~tanga Tūingoa, Tūmahi Poro
intersect, intersection (takenga mai: pūtahi – join, meet)
base (of a geometrical figure)
outcome (takenga mai: puta – come forth, come out) (kupu kē atu: hua, otinga)
radius (takenga mai: pū – centre; toro – stretch forth, extend)
degree (angle and temperature) (tohu: º) (takenga mai: putu - lie one upon another) (kupu kē atu: tākiri [kupu mino])
collinear points
cylinder (takenga mai: rango – roller)
oblique cylinder
(mathematical) problem (takenga mai: rapa – seek, look for)
line
perpendicular line
line of symmetry
oblique line (kupu kē atu: rārangi tītaha)
horizontal line
curved line
tangential line
line segment
vertical line
intersecting lines, concurrent lines
concurrent lines, intersecting lines
divergent lines
straight line
convergent lines
bisector, median (of a triangle) (takenga mai: rārangi - line; weherua - to divide in two)
rārangi weherua hāngai Tūingoa
perpendicular bisector
parallel line
transversal
net (of a solid figure) (takenga mai: raumata – mesh of a net)
transformation sequence
geometric strategy
similar (in proportion)
regular (shape) (kupu kē atu: ōrite)
length, long
rōpinepine Tūingoa, Tūmahi Poro
tesselate, tessellation, tiling, mosiac (takenga mai: rōpine – place close together)
set square (takenga mai: tā –to draw; hāngai [koki hāngai] – right angle)
diamond shape (takenga mai: He kupu mino.) (kupu kē atu: tapawhā whakarara rite, whakarara rite)
region (of space or time)
edge, side (kupu kē atu: taha)
adjacent side
opposite side
decagon (regular)
tapa-tekau mā rua (rite) Tūingoa
dodecagon (regular)
segment (takenga mai: tapa – cut, split)
minor segment
major segment
nonagon (regular)
hexagon (regular) (takenga mai: tapa - side; ono - six; rite - similar, alike)
trapezium (takenga mai: tapa [tapawhā] – quadrilateral; rara [whakarara] – parallel)
isosceles trapezium
polygon (regular) (takenga mai: tapa – margin, edge; rau –many; rite – alike, similar)
pentagon (regular)
triangle
right-angled triangle, right triangle
scalene triangle
obtuse-angled triangle
acute-angled triangle
curvilinear triangle
equilateral triangle
isosceles triangle
octagon (regular) (takenga mai: tapa - side; waru - eight; rite - similar, alike)
quadrilateral (takenga mai: tapa – margin, edge; whā – four)
rectangle, oblong
tapawhā pūtahi porowhita Tūingoa
cyclic quadrilateral
square
polyomino (takenga mai: tapawhā rite - square; rau - many)
pentomino (takenga mai: tapawhā rite - square; rima - five)
parallelogram
tapawhā whakarara rite Tūingoa
rhombus, diamond shape (kupu kē atu: whakarara rite, taimana)
heptagon (regular)
compass (for drawing circles) (takenga mai: tā –to draw; porowhita – circle) (kupu kē atu: taputapu tuhi porowhita)
apparatus, device, equipment, instrument, tool
annulus (takenga mai: tarawhiti - to encircle, hoop, ring; ahu-2 - 2-dimensional) (kupu kē atu: tarawhiti papatahi)
torus (takenga mai: tarawhiti – hoop, ring, encircle; ahu-3 - 3-dimensional)
hypotenuse (takenga mai: tāroa – long)
tārua ~tia ~tanga Tūingoa, Tūmahi Whiti
copy, repeat
order of symmetry
opposite (kupu kē atu: anganui)
pattern
two-dimensional model (whakapotonga: tauira ahu-2)
three-dimensional model (whakapotonga: tauira ahu-3)
concrete model (takenga mai: ōkiko - physical; ō - pertaining to; kiko - body, substance)
tāwhai ~tia ~tanga Tūingoa, Tūmahi Whiti
trace (takenga mai: tawhai - to imitate) (kupu kē atu: whaituhi)
altitude, height, high, tall (kupu kē atu: tāroaroa [of a person], tiketike)
limit of accuracy (takenga mai: tepe – boundary, limit; tika – correct)
apex (takenga mai: tihi – summit, top, peak)
accurate, correct, valid (kupu kē atu: tōtika)
method, technique, convention, meaning
tirohanga (mai i te taha) matau Tūingoa
right side view
tirohanga (mai i te taha) mauī Tūingoa
left side view
front view
tirohanga (mai i) muri Tūingoa
rear view
tirohanga (mai i) raro Tūingoa
bottom view
tirohanga (mai i) runga Tūmahi Whiti
plan view (kupu kē atu: tirohanga ā-manu, hoahoa ā-manu)
shear (takenga mai: tītaha – lean to one side, slant)
apothem (takenga mai: toro – stretch forth, extend; pū – centre; hāngai – perpendicular)
straight
axis (takenga mai: tuaka – midrib of a leaf)
axis of symmetry
tūhura ~tia ~tanga Tūingoa, Tūmahi Whiti
investigate, investigation
grid
isometric grid
theorem of Pythagorus
whole (kupu kē atu: katoa)
isosceles (takenga mai: wae – leg, foot; rite – alike, corresponding)
build, construct, create, generate
weherua ~tia Tūingoa, Tūmahi Whiti, Tūāhua
bisect (takenga mai: wehe – divide; rua – two)
mental image
representation
whakapae ~tia Tūingoa, Tūmahi Whiti
hypothesis
whakapeka ~tia ~ nga Tūingoa, Tūmahi Whiti, Tūāhua
distort, distortion
parallel (takenga mai: whakarara – mark in parallel lines)
whakarōpū ~tia ~ tanga Tūingoa, Tūmahi Whiti
classify, group
clockwise (kupu kē atu: ā-karaka)
breadth, wide, width
cosine (tohu: 
) (takenga mai: whenu – warp of a flax garment)
inverse cosine (tohu: 
)
concertina (takenga mai: whētui – fold; hokohoko – alternate)
diameter (takenga mai: whiti – cross over, reach the other side)