by Bill Lauritzen
Algebra = Symbols (or Abstract Math)
| associative property | 7 | grouping property | 5 |
| commutative property | 7 | switching or order property | 5 |
| distributive property | 7 | spreading property | 5 |
| substitution | 4 | trade | 1 |
| identity element of mult. | 13 | same-same for times | 4 |
| identity element of add. | 11 | same-same for add | 4 |
| inequality | 5 | no-match | 2 |
| unknown | 2 | not-known | 2 |
| variable | 4 | changeable | 3 |
| coefficient | 4 | front | 1 |
| diagonal | 4 | across | 2 |
| equiangular | 5 | match-niked | 2 |
| angle bisector | 5 | nik halfer | 3 |
| exponent | 3 | pow | 1 |
| origin | 3 | start | 1 |
| abscissa | 3 | x-line | 2 |
| ordinate | 3 | y-line | 2 |
| coordinates | 4 | facets | 2 |
| x coordinate | 5 | x facet | 3 |
| intercept | 3 | cut | 1 |
| y-axis | 3 | y-line | 2 |
| x-axis | 3 | x-line | 2 |
| y-intercept | 4 | y-cut | 2 |
| x-intercept | 4 | x-cut | 2 |
| quadrant | 2 | fourth | 1 |
| domain | 2 | home | 1 |
| range | 1 | -- | 1 |
| linear equation | 6 | line-match | 2 |
| quadratic | 3 | twoed or pow-two | 1 |
| quadratic equation | 6 | pow-two match | 1 |
| parabola | 4 | throw | 1 |
| hyperbola | 4 | over-throw | 2 |
| eccentricity | 5 | ovalness | 3 |
| prime number | 3 | -- | 3 |
| composite number | 5 | patterned number | 4 |
| highly composite | 5 | versatile | 2 |
| sequence | 2 | follow | 2 |
| sequential | 3 | following | 3 |
| arithmetic sequence | 6 | add-same | 2 |
| geometric sequence | 6 | times-same | 2 |
| series | 2 | -- | 2 |
| binomial theorem | 6 | 2-term rule | 2 |
| completing the square | 5 | finish the twoed | 4 |
Properties = Facts
| properties of equality | 8 | balance fact | 4 |
| transitive property | 6 | swap fact | 2 |
| substitution property | 7 | swap fact* | 2 |
| addition property | 6 | add fact | 2 |
| multiplication property | 8 | times fact | 2 |
| distributive property | 7 | spreading fact | 3 |
| reflexive property (A=A) | 6 | is fact | 2 |
| symmetric property (if A=B, then B=A) | 6 | turn-same fact | 3 |
| symmetric property (if A=B, then B=A) | 6 | turn-same fact | 3 |
| the inverse (p>q, not p>not q) | 3 | the not | 2 |
| the converse (p>q, q>p) | 3 | the flip | 3 |
| conditional statement | 6 | if-say | 2 |
| complement | 3 | fill | 1 |
* transitive and substitution are not both needed
Trigonometry = Three-Nik Zooming
| trigonometric tables | 7 | 3-nik tables | 4 |
| trigonometric ratios | 7 | three-nik "to"s | 3 |
| adjacent | 3 | by | 1 |
| opposite | 3 | far | 1 |
| hypotenuse | 4 | long | 1 |
sine ratio = far/long or FoL [far side over long side]
cosine ratio = by/long or BoL [by side over long side]
tangent ratio = far/by or FoB [far side over by side]
cosecant ratio = long/far or LoF [long side over far side]
secant ratio (4) = long/by or LoB [long side over by side]
cotangent ratio (5) = by/far or BoF [by side over far side]
[sin/cos = tan, this is immediately evident when you write FoL/BoL = FoB]
Thus:
sin = fol (far over long) or f:l or f/l or F/L or F:L
| sin | 1 | fol (far over long) | 1 |
| cos | 2 | bol | 1 |
| tan | 2 | fob | 1 |
| csc | 3 | lof | 1 |
| sec | 2 | lob | 1 |
| cot | 3 | bof | 1 |
The relationships of the various triangle ratios (trigonometric ratios) are immediately evident. With fol used for sin there would be no more looking up sin to see that it is the opposite over the hypotenuse. It is immediately apparent that it is the far side over the long side of a right 3-nik (triangle).
Also, fob = fol/bol, and fol 30 = 0.5, bol 30 = 0.866, and fob 30 = 0.577.
Calculus = Curve Science or Curves
(which is a sub-study of Shapes)
| circle | 2 | ring | 1 |
| ring | 1 | fat-ring | 2 |
| ellipse | 2 | oval | 1 |
| parabola | 4 | throw | 1 |
| hyperbola | 4 | far-throw | 2 |
| tractrix | 2 | right tow | 1 |
| bicyclix | 3 | two-wheel | 2 |
| catenary | 4 | hang | 1 |
| brachistochrone (curve of fastest descent) | 4 | fast curve | 2 |
| sine curve | 2 | fol curve | 2 |
| cosine curve | 3 | bol curve | 2 |
| ellipsoid | 3 | oval-oid | 3 |
| paraboloid | 4 | throw-oid | 2 |
| catenoid | 3 | hang-oid | 2 |
| pseudosphere | 3 | horn | 1 |
| torus | 2 | donut | 2 |
| curve segment | 3 | curvet | 2 |
| cycloid | 2 | roll-curve | 2 |
| function | 2 | in-out or IO | 1 |
| limit | 2 | stop | 1 |
| infinitesimal | 5 | smallest | 2 |
| continuous | 4 | unbroken | 3 |
| relation | 3 | -- | 3 |
| differentiation | 6 | slope-finding* | 3 |
| differential | 5 | slope or touch-line | 1 |
| integration | 4 | fill-finding* | 3 |
| integral | 3 | whole | 1 |
| maxima | 3 | highs | 1 |
| integration | 4 | grouping | 2 |
* Dr. Eli Pine recommended the terms slope-finding and area-finding
| minima | 3 | lows | 1 |
| maximum | 3 | high | 1 |
| minimum | 3 | low | 1 |
| derivative | 4 | branch | 1 |
| first derivative | first branch | 5 | 2 |
Measurement
| measure | 2 | measure or how-much | 2 |
| meter | 2 | -- | 1 |
| decimeter | 4 | teni-meter | 3 |
| centimeter | 4 | huni-meter | 3 |
| millimeter | 4 | thou-meter | 3 |
| kilometer | 4 | thousand-meter | 4 |
| cubic centimeter | 6 | huni-meter box | 4 |
| metric system | 4 | ten system | 3 |
Statistics = Fact-Numbers
| measures of central tendency | 8 | landmarks | 2 |
| mean | 1 | average | 2 |
| mode | 1 | often | 2 |
| median | 3 | middle | 2 |
| minimum | 3 | lowest | 2 |
| maximum | 3 | highest | 2 |
| range | 1 | -- | 1 |
| outlier | 3 | -- | 3 |
| probability | 5 | chance | 1 |
| desired outcomes | 5 | wants | 1 |
| possible outcomes | 5 | cans | 1 |
| distribution | 4 | spread | 1 |
| standard deviation | 6 | standard spread | 3 |
| quartiles | 2 | fourths | 1 |
| histogram | 3 | past-spread* | 2 |
| normal distribution | 6 | normal spread | 3 |
| descriptive statistics | 6 | number-fact showing | 5 |
| inferential statistics | 7 | number-fact conclusions | 6 |
| correlation | 4 | link | 1 |
| variance | 3 | shift | 1 |
| frequency | 3 | repeat | 2 |
| correlation | 4 | like | 1 |
| experiment | 4 | try** | 1 |
| observation | 4 | see | 1 |
| hypothesis | 4 | say | 1 |
| variable | 4 | changeable | 3 |
* a histogram is a statistical summary of past occurrences.
** see my paper on "Useable Science: The Try-See-Say Cycle" at my web site.
| dependent variable | 7 | dependent variable | 4 |
| independent variable | 8 | unfixed changeable | 5 |
| experimental design or protocol | 3 | try-plan | 2 |
| analysis of variance | 8 | shift breakdown | 3 |
| mutually exclusive | 7 | no-both | 2 |
Dynamic Math = Changing Patterns
center of gravity (barycentric point) = balance point or center of mass
| Total Syllables: 1413 | Total Syllables: 770 |
Quiz:
Match these SpeakEasy sentences with their traditional math sentences.
SpeakEasy
1) The fill of an even-box is the length of a side pow three.
2) The around of a ring balances the across times 3.14.
3) The fence of a right four-nik of side 3 evens 12.
4) The right-fill of 30 twiks evens 60.
5) In a right three-nik the long matches the sum of the legs two’d.
6) The fol of a right three-nik matches the far side over the long side.
7) A blunt nik is a nik whose measure is greater than 90 twiks but less than 180 twiks.
8) Two niks are called by-niks if, and only if, they have the same nik-dot and a same side.
9) A pair of not-by-niks formed by two crossing lines is called a pair of facing niks.
10) Facing niks match.
Traditional
A) The perimeter of a square of side 3 equals 12.
B) Vertical angles are equal.
C) In a right triangle the hypotenuse squared equals the sum of the legs squared
D) The volume of a cube is the length of a side to the third power.
E) An obtuse angle is an angle whose measure is greater than 90 degrees but less than 180 degrees.
F) The circumference of a circle equals the diameter times 3.14
G) The complement of 30 degrees equals 60.
H) The sin of a right triangle equals the opposite side over the hypotenuse.
I) Two angles are called adjacent angles if, and only if, they have a common vertex and a common side lying between them.
J) A pair of nonadjacent angles formed by two intersecting lines is called a pair of vertical angles.
Answers:
1-D
2-F
3-A
4-G
5-C
6-H
7-E
8-I
9-J
10-B