; ; ; ; Updated in 2024 : January : 27th (Saturday) : MATH a.k.a. Mathematics ;

alike; equal; similar; Radical251;

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a side of Geometric Shape; e.g.

a side of Geometric Shape (GS) esp. of a rectangle, of a triangle, of a polygon, ... ;

( Shape, shape, shape, shape, shape) : ( a side of Geometric Shape) ... ;

("Using Polygon Method, a.k.a. Triangle Method"), also see: Numbers in Computing e.g. (( one, the only entity), ( halves (plural Usage), a.k.a. one half (singular Usage)), ( minus one, a.k.a. negative one), ( two, two), ( actually express, a.k.a. denoting is intended to be, a.k.a. indicated), ( one part of three equal parts, one third), ( a quarter, a.k.a. one-fourth, a.k.a. 1 out of four equal parts of the entity)), ... ;

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(b u n s h i Numerator, b u n b o Denominator), e.g. Number above the line in a common fraction / Number below the line in a common fraction, another example would be: b u n s u Fraction of (2/3) can be using for 6 surfaced DEE Box in Z-index, ... ; Also see: Optics; Remark: depending upon OEM 's embedded devices, quality of the mantissa point may vary;

chizu Map; Radical714;

division operator; Also see: Operator IFF Mathematics; Radical286;

equal; Radical211;

Equilibrium     Equilibrium     Equilibrium; Also see: e Computer; Physics Law 141;

float; floating; Radical960;

in Mathematics, relationship between 2 numbers is; Radical102;

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Inverse Cosine Function; e.g.

Inverse Cosine Function doko WHERE y = (cos^(-1)) x, also see: Physics Law 232, (Yellowish Variations, Yellowish Variations) .  .  . ;

I wrote: since strings (e.g. moon wave (s) are coming naturally (our earth)), do you think that 1 Navy Color string is good enough to define?

well trained kids!! replied: No. Sir.

I wrote: (defining, finding, knowing) directional gravity spots begin; 2024 design model, for normal Yellowish Variation, also see: Japanese . Syllabary . HTML ; after (defining, finding, knowing) gravity spots worldwide, don't tell anyone, keep IT for yourselves (one of the top military secrets), because you don't want to deal with (gangsters, terrorists, undercover agents), and remember our earth is not simple like WHAT I think;

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natural Infix Fraction; e.g.

Also see: natural Infix Fractions;

I wrote: in 2024, I created "natural Infix Fractions .HTML," doshite Why?

well trained kids!! replied: Hmm!! Umm!! , Using Polygon Method, a.k.a. Triangle Method, and prior to realizing IT, Numbers in Computing should be read sir;

I wrote: Yes. LASER (lights as polygon, lights as triangle) ... , and don't forget to use 15 degree by SQRT2 longitudes, IFF Space War (Satellite) .  .  . ; natural Infix Fractions are very useful, kuru kuru WHILE handling ("86" Architecture, Nanobot Programming structural, Perfect Square, Pi, 2Pi, Structural Diamond, ... ) .  .  . ;

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perimeter; Radical510;

sheaf; Radical636;

sum (Mathematics); Radical850;

two; Radical7;

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well trained kids!! replied: in addition to "AB/BC," is there CD, DVD, D QR, ... sir?

I wrote: 1st to realize & understand Referenced Books (e.g. CD, DVD, in addition to "AB/BC") ... ; 2nd to realize & understand (drawings, images, patterns, photos, pictures) of yours (e.g. 18000+ items As Content within this DOMAIN and (each item, every item) has its own colorful, meaningful, ... ); 3rd to R&D e.g. Bamboo Stem Factor R&D has begun since May, 2023, for BLI Auto Adjustment (DNA _Origami, Nanobot Programming) on human beings livable moons ... ;

ア メ リ カ   緬 甸   .網     mathematical Bamboo Stem R&D;

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Time . Space . Action: SYNC, A S Y N, ... , Mathematics, some people like, some people dislike, you do not need several years of learning mathematics to know 5W1H of mathematics, but you may need a few hours of teaching from a genuine math teacher to understand all about mathematics; After understanding all about mathematics, and then time to do your ...  Do your own math, bring a common calculator, press 2, i.e. in ACT1 stage, and then press square root sign, and then keep pressing again and again √ square root 22 times, and notice that result prompts 1, and then try to mathematically prove that HOW a calculator slices time period, WHY only 22 times, (WHERE is 2 * 7 (also see: 4_Planets_Prediction)), and so on ... ; In Korea, average high school students can do math without using calculator, can perform up to 99 * 99; Try to compete math to Korea's new generation ... ; Try to compete, try to participate in the world's open math contests; Since 1985, 1 + 1 = 1 can be proved by algebra, therefore be very careful in equations, formulations, ... ;   The following information contents express the current up-to-date basic-understanding of mathematics;

two sequences of bits (floating point mode (digits in the number, and its exponent prompts position of the radix point)) i.e. floating points ... ;

using mantissa points to solve problems of infinity;

using Defusing Remote Heat Sensing (also see: Gene Therapy System Basic Symbol) to solve problems of "cracks" WHICH kill symmetries;

( 2 - 4) Method, also see: this _DOMAIN _'s _position _Info _with _Timestamp;

( forever, e i e n n i Forever, Forever, Forever), a.k.a. infinity (e.g. Symbol: (∞ INFINITY) means forever);

I wrote: HOW to solve SQRT2 floating points (±98) 's ∞ INFINITY of floating?

well trained kids!! replied: using mantissa points to solve problems of infinity (e.g. using engineering notations: 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, ... ) ; Umm!! Umm!! 10 is (Local), 100 is (Remote), 1000 is (Global), 10000 is (Universal), 100000 if (Yellowish Variation), ... ;

I wrote: in DVD (doesn't matter whether plus or minus) design model in common, WHAT would be the (∞ INFINITY) a.k.a. ( forever, e i e n n i Forever, Forever, Forever) for each DVD?

well trained kids!! replied: for each DVD in common, ((∞ INFINITY) = (4.7 GB, 120 minutes)) for each DVD sir; Remark: 16x Speed (16x is referring to 1995s' 150x to PC I IDE bus); We don't confuse, Umm!! Umm!!  

2 inconsistencies in math are problems of infinity and problems of "cracks" WHICH kill symmetries;  

Consider the image which represents dark, earth, sun altogether, this one & only the Sun [ just before noise in ACT2, the red line at top, visible by space imaging there is nothing out there except 4 planet prediction, just before dawn in ACT1, ... ] image might be the 1st crack of our universe's cracks, and yellow colored character represents the Earth (EM, EMI, normal yellowish a.k.a. no yellowish variation, yellow core), approx. 35+ years old information of the Sun in our universe; Only restricted people from higher civilization can solve ... ; The whole character Red + Yellow is king. And, notice that especially in this "the 1st crack of our universe", the gap exists, and the 1 gap might be for 1 tangent a@t 1 time of our universe a@t 1 dimension IFF dimensional hyperspace craft's retrospective in 1D (also see: ..\..\Info\index). WHY red color as the 1st crack of our universe? Human beings perceive? also read Buddha Abhidhamma (also see: ..\..\Buddha\Book\Book).

IFF problems of infinity exists (e.g.

floating points of square root 2 ≡ decimal expansion ≡ problems of infinity a.k.a. SQRT2;
floating points of square root 3 ≡ decimal expansion ≡ problems of infinity a.k.a. SQRT3),

use mantissa point doko WHERE truncating points are at e.g. (2^3) a.k.a. 8, (2^4) a.k.a. 16, (2^5) a.k.a. 32, (2^6) a.k.a. 64, (2^7) a.k.a. 128, (2^8) a.k.a. 256, (2^9) a.k.a. 512, 1K a.k.a. (2^10) a.k.a. 1024, (2^11) a.k.a. 2048, (2^12) a.k.a. 4096, (2^13) a.k.a. 8192, (2^14) a.k.a. 16384, (2^15) a.k.a. 32768, (2^16) a.k.a. 65536, (2^17) a.k.a. 131072, (2^18) a.k.a. 262144, (2^19) a.k.a. 524288, (2^20) a.k.a. 1048576, ... ; notice that C Sequence Number (structural) WHICH is beyond (dimensional, directional, numerological) starts at 2^20, 2^30, 2^40, ... ; also notice that 20 (i.e. middle JUN) water drops alike characters, inside the catalog of syllables (NIPPON, also see: Nippon Syllabary);

for each DEE (Dark Energy Engineering) pattern, DEE can be defined in mathematics, also see: Monbusho level knowledge enhancement 2, idea ♯ 216, defined DEE Patterns; for well trained kids! , you can define your own equations and formulations, ... ; good luck to you (e.g. you can have your own Gravity Dimension Computer, e.g. you can have your own imaginary hyper space crafts, e.g. you can have your own space system) ; notice that this DOMAIN has been designed, using graphics and keywords;

Integral; Remark: think THAT upper pi-by-two and lower pi-by-two are approx. forty five degree parallel at the edge (s) of vertical DEE line (upper pi is one hundred and eighty degree different to lower pi), doko WHERE sekibun Integral, necessary to make a whole complete (i.e. from zero to infinity), e.g. DEE in our universe with peaceful & tranquil human beings livable moons' orbital (s) ... ;

K-Theory and its D-b r a n e s, M-Theory and its strings, Unified Strings theory, ... , are all try to prove particles' vectors bundles ... ;

N C G, Non Commutative Geometry: common usages are "metric-tensor" to determine 2 points in space's length for each abstract notion of manifold, quantum field theory and its space-time, billions dollars cost so called non-trivial quantum relationship in commutation is N C G; Nuclear power of Western civilization was in 20th century only; To accomplish the ACT 2 stage, all nuclear power must be demolished and destroyed unconditionally; also see: worm₌hole; admiral; commander; Radical344;

commutative, (group of quantities) 's condition, kuru kuru WHILE using Operator, the defined condition prompts the same result e.g. ((x + y = y + x), (x - y = y - x), (x * y = y * x), (a/b = b/a)), whatsoever order of the quantities are e.g. "a" as quantity, "b" As Quantity; Also see: Physics Law 135, commutative;

Super Symmetry & Super Gravity, must learn Chinese characters, because i.e. artificial energies, artificial lights, pressure machine engines, gravity machines, M R I (s) and P M D, remote-virtual-electricity, vertical EM scanner (s) and reflector (s), laser (s), ... , since 1980s ;

Characteristic classes, Fiber bundles, and Index theorems, ... , are related to dimensional space, hyperspace, ... ; Symmetry for each dimension; And very advanced, very limited, very classified, ... ;

Also see: Relational Algebra, RDBMS, since 1970s, along with index theorems ... ;

For basic understanding of WHAT is super symmetry, also see: Monbusho level knowledge enhancement idea ♯ 146; Super Symmetry;

Homology vs. H o m o t o p y  

Homological common usages are 1D circle, 2D circular disk, boundary, chains, h o m o t o p y complexes, simplexes, ... ;

H o m o t o p y is a relation between 2 mappings; H o m o t o p y common usages are contractibility, hole [also see: worm₌hole], h o m o t o p i c mapped loop, h o m o t o p y groups, loop, path, ... ; In Java language, 2 common mappings are J P A inheritance mapping, and J P A relationship mapping;

Remark: after understanding a path to be integrated, partially differential to each Left, and Right as a chain (s), and then try to understand 2-spin strings interaction, ... ; Also see: Pairs of sticks;

ACT2 and ACT3 objects are (2 and 3) vector directions, ACT2 and ACT3 2*5 JUN time, ACT1 and ACT2 (2*7) lunar co-existences [full moon day & no moon day, also see: \Info\Help\ USA Myanmar], ACT3 3 to 1 dimensions, ACT1, ACT2 and ACT3 4 planets prediction [2500+ years old information in Buddha calendar], ACT2 distance to SUN < distance to MOON, ... , and, ACT2 and ACT3 subjects are ACT2 2 times daily tidal water, ACT1 holes as no existence of the SUN (also see: no moon day), ACT3 horizontal and sectional gray scales [also see: \Info\index], ACT1 and ACT2 stars as no existence of the SUN, ACT3 very very very dark environment [also see: 4PP + JUN = 6, and 6 has been defined in Abhidhamma], ... ; Answer would be: the one the only the sun is gravity spot (please do not create gravity spot larger than the sun), and 1 way DEE and BF2 is because of our earth's momentum, and our earth is one of the moons, ... (also see: My Imaginary Space) ... ;

IFF (2*6) dimensional, also see: 8;

Differential Forms vs. Differential Geometry

Differential Forms: common usages are dynamics, integral-able conditions, ... ;

Differential Geometry: common usages are coordinate systems, covariant derivatives, metrics, curvature in coordinate, curvature in non-coordinate, ... ;

Lie Groups (also known as language of symmetry; also read the book: Page 103, Beyond Einstein, M i c h i o K a k u and Jennifer Thompson, 1995): common usages are differentiable-manifold, killed vectors, lie-algebras representations, lie-derivatives, lie-matrix representations, ... ; Also see: 2-point distance to n-point distance;

IFF ACT2 ACT3 space mathematicians, also see: 2,3 dimensional distribution formula designing and engineering, [ for near future ACT2 space public traveling ... ];

O means Orthogonal; catalog groups of types into 7; 1 class is called O (N); atom itself is O ( 3); In 1800s, S o p h u s Lie (Norwegian) discovered a set of symmetries called SU (N) WHICH rotates complex number e.g. SU (1) with 1 photon, e.g. SU (2) with 1 photo and 1 neutron; Notice THAT prior to superstrings (1 word would be "spin"); (SU (2) x U (1)) with 1 electron and 1 neutrino; SU (3) rotates 3 sub nuclear particles; SU ( 5), the smallest GUT theory (1 electron, 1 neutrino, 3 quark); IFF N (quark) and then SU (N);  E (N) WHERE N <= 8 also known as E(8) group, and superstrings' symmetry begins, and higher dimensions begins e.g. 8, 10, 26, ... ; Unified Theory adapted Lie Groups in 1900s;

But, since 2000s, this DOMAIN has implemented (e.g. C Sequence Number) both 10 (2*5, d a s s a, 10, ... , d a s s a became desu thousand years ago) and 26 (numerological dimension) for thousands of years in software approach (hardware approach is intentionally left for oriental e.g. NIPPON; notice that Myanmar has been non-semi-conductor nation and this DOMAIN developer is out of hardware design knowledge e.g. HOW to embed Idea Processor into GPS ? e.g. HOW to embed GPS into computer? e.g. HOW to embed all basic calculator, dictionary, and translator to be AI ? ) e.g. web site as Triangulation System in the Internet, therefore, please do not change its aesthetics (also see: philosophy); Therefore, 21st century's power e.g. Gravity & IT, e.g. Manmade Global Weather (service), e.g. directional gravity for elevating automotives, ... are military top secrets ... , therefore, NOT available to public; WHICH is beyond stars are groups in constellations (also known as Lie Groups);

2100s predictions: gene therapy systems, gravity dimension computers, teleportation methods, ... ; There will be Rakhine (an ethnic tribe of Union of Myanmar) for sure WHO will ... ;

Analysis of Complex vs. Analysis of Real

Real: common usages are real function as isomorphism, real function as fix-point (s), and real function as mapping; Topologies such as neighborhoods, homeomorphisms, invariants, sets, ... ;

Complex: common usages are complex variables, space, strings representing as functions, surfaces, ... ; Also see: Complexity Region;

Probability & Statistics

Quantum mechanics in physics proposed, and demanded probability and statistics; Common usages are mean, quantitative counting of distinguishable objects, qualitative counting of distinguishable objects, quantitative counting of indistinguishable objects, qualitative counting of indistinguishable objects, variance, ... ;

Approximation Method

Fuzzy set was condemned in 20th century by western nations, but unofficially, however eastern nations accepted; In 21st century, so many proofs of so many new technologies make people around the globe convince that fuzzy set is the way to do controls; Whenever a problem cannot be solved, approximation method is needed; Large perturbation +, saddle-point integration, series' expansions in power, small perturbation -, ... are not in exact-closed-form, therefore, cleverly guessing of approx. ... ;

IFF distance approximation, also see: Monbusho level knowledge enhancement 1, idea ♯ 178, Distance Approximation with C Sequence Number, Math approach, HOW gravity spots as induction in 1 computer ... ;

Differential Equation: Ordinary vs. Partial

Function of 2 variables can be defined as y = f (x)   OR   x = f (y); doko WHERE y can be defined by function of x,   OR   x can be defined by function of y; IFF y = f (x) can also be written as d y = f' (x) d x, to do increment-approximation of the given function y = f (x) as d derivative of the function times  times = * = x = multiplication, ...  the increment of independent variable;

For example, d x = f' (t) d t means increment-approximation time t assuming that orbital synchronization time t of the given function i.e. x = f (t) as d derivative of the function * the increment of independent variable in 3-to-1 dimension as x,  WHERE in our universe, 3 planets' almost tangent valued gravitational waves cause 1 earth's full moon day ... ; In this case, derivative d t is partially calculated for partially delay time, partially artificial energies, partially artificial lights, and so on ... ; Also see: Time . Space's 3 for 3 dots in our universe ... ;

Algebra: Linear

linear equation must be express 1st, i.e. a_i1 x₁ + a_i2 x₂ + a_i3 x₃ + ... + a_in-1 x_n-1 + a _in x _n = c _i; And then express the displacements either in matrices, or in vectors; Properties of abstract matrices are asymmetric, characteristic equation, determinant, inverse, symmetric, unitary, ... ;

( geometry, geometry, geometry, geometry, geometry), property & relation of (Dimensional, Line, Point, Solid, Surface) ... ; Geometry: Analytical

Algebra and geometry; Geometric entities such as conic-sections, planes [such as: 2D plane, 3D plane, Polar plane, spherical coordinate, X Y coordinate, X Y plane, ... ], Sphere think circle in 2D becomes sphere in 3D, so called solid geometric entity, ... ; 5W1H algebraic equations for each geometric entity is called analytical geometry;

mathematical operators (e.g. ∂∆∏∑−∕∙√∞∟∩∫≈≠≡≤≥); Also see: AI FONT;

Multiple Variables vs. Single Variable

Multiple variables' abstract functions, i.e. f (i, j, k, ...); Thus d derivatives becomes in partial, or/and, in a whole; In 2D, 3D space, integration of a path, integration onto a surface, are all based on directional d derivatives; Also see: e v o l u t e, and understand a curve's tangent (s) cause another curve, after understanding the directional d derivatives, partially or/and whole functionalities become designers' mathematicians' engineers' developers' 5W1H ...  concepts, ideas, logics, and so on ... ;

Single variable's abstract functions;

Transform: patterns can be transformed to-and-from between analog and digital; doko   WHERE analog is a.k.a. harmonic motion, and digital is a.k.a. discrete (isolated set of points ( dots)); Schematic Symbols' SHARP 's D A L e.g. , , , , , , , , ... ; transform e.g. (analog digital) also see: Fourier; pattern;

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( INV, INV, INV, INV), inverse function, a function THAT 's reversing another function;

e.g. ( DEG . cos) 's INV is cos^-1;
e.g. ( DEG . e) 's INV is ( RAD . e);
e.g. ( DEG . ln) 's INV is e^x;
e.g. ( DEG . log) 's INV is 10^x;
e.g. ( DEG . sin) 's INV is sin^-1;
e.g. ( DEG . tan) 's INV is tan^-1;
e.g. ( DEG . !) 's INV is ( RAD . !);
e.g. ( DEG . π) 's INV is ( RAD . π);
e.g. ( DEG . ^) 's INV is ( RAD . ^);
e.g. ( DEG . "(") 's INV is ( RAD . "(");
e.g. ( DEG . ")") 's INV is ( RAD . ")");
e.g. ( DEG . √) 's INV is x^2;

INV is INVERSE, i.e. math usage ... ; Also see: Mathematics;
INV is INVOICE, i.e. business usage ... ; Also see: Biz;

I wrote: I've created a picture i.e. INVERSE, and I've a quiz: regarding (our earth, our moon), if I'm on the moon, HOW would the "INVERSE" would be?

well trained kids! replied: very easy quiz; since (area, environment) has lots of (Silver), Blue and Green are reversing each other sir;

I wrote: yes. so desu n a l ... ; don't forget THAT (Yellow) and (Red) are also reversing ... ;

( INV, INV, INV, INV), also see: 9iComputer; Mathematical Calculations; Physics Law 181;

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Remark: Idea Processor (think THAT minus is like differential if compare to plus is like integral) ... ; Also see: Mathematics;

Trigonometry

Common usages are right-triangle (s), trigonometric functions of sine, cosine, tangent, ... ;

e.g. sin Θ, also see: 6sComputer;
e.g. cos Θ, also see: 1cComputer;
e.g. tan Θ, also see: 8tComputer;
e.g. c s c Θ, also see: 7cComputer;
e.g. sec Θ, also see: 9sComputer;
e.g. cot Θ, also see: 2cComputer;

Geometry

2D, 3D, ... , Common usages are geometric shapes in 2D, geometric shapes in flat, 2D X Y planes, similarity, symmetry, ... ;

Algebra

Linear equation of form y = ax + b;

Quadratic equation of form y = ax² + b x + c;

For advanced mathematicians only: solve and prove that the statement 1 + 1 = 1 can be proved by algebra, in a characteristic of Space . Action's 2-spin-strings, however, WHEN Time . Space concerns in ACT2, or ACT3 stages, HOW to prove 2 fuzzy sets { ... can also be proved as 1 f (x) of 1 fuzzy set { ... ; Question is whether Time . Space OR Timeless?

For Monbusho level developers only: 2500+ years old Myanmar's original document has been based on 7, and 2 * 7, in lunar orbits, 22 times of square root of 2, result prompts 1, mathematically prove that the 4 Planets Prediction diff in Space Time vs. Natural Time; WHY 22 times, HOW 2 and 7 relates to each other, ...

...

IFF Mathematics : for each circle, orthogonal polynomials limit theorems (a.k.a. S z e g o), ... ; Also see: Optics;

Basic mathematics Be very careful, since 1985, 1+1=1 can be mathematically proved by algebra

Analytical skill enhancement by studying relationship among point, line, angle, and plane; Parallel, NOT parallel proofs; Postulated parallel; Decision and reasoning skill enhancement of fuzzy logic, illogical logic, logical logic, relative truth logic, universal truth logic; Direct proof vs. indirect proof [Also see: ACT1 Theoretical Law To ACT2]; Triangle congruence, property, and similarity; Equality property of triangle vs. Inequality property of triangle; Equilateral triangle, Isosceles triangle, centralized triangle; A S A S A S S S S triangle congruence; Quadrilateral & polygon; Polygon property; Quadrilateral property; Area analysis of perimeter of quadrilateral; Circle vs. arc, angle, chord, tangent, ... ;

2D geometric figures; Point, and then displacement of points, Line; Plane & Coordinate; Angle; Triangle; Quadrilateral; 2D area vs. 2D perimeter geometric figure; Area vs. Perimeter; Unit & Dimensional Area; Parallelogram area vs. Parallelogram perimeter; Trapezoid area vs. Trapezoid perimeter; Circle, Cycle, Eccentric cycle; 22/7 circular part & its measurement; 3D geometric figures; Polyhedral; Platonic solid & sphere; Surface area vs. Volume [Balancing: non-object vs. object]; Dimensional state of solid; Symmetry vs. Balance; Symmetrical line & Tessellation; Kinetic motive rotation; Reflection, Glide reflection, and basic translational energy; [ACT3 coordinate-less D number];

dividend: Number to be divided by another number, e.g. WHERE (2 As Dividend, 6 As Divisor, 0.333333333333333333333333333333333 As Quotient) ... ; business usage, also see: Biz; Stock;

I wrote: if I say 1.384114728, WHAT would that be related to mathematics? hint: ^{SHIFT 3}_{√ ((15 * √2) /2)} ;

well trained kids!! replied: Hmm!! Umm!! regarding 2, and 3, IT could be related to 108 configuration sir, e.g. (18) is equal to (2 ^. 3 ^. 3), doko WHERE √18 = √ (2 ^. 3 ^. 3) = √ (2 ^. 9) = (√9 ^. √2) = 3 √2 so, 13 (your hidden system) = 18 - 5 (each edge) ... ; Umm!! Hmm!! also see: 2; 3; 108 configuration; Mathematics; Time; if we SQRT2 (1.414213562) 1st, And Then, multiply by 3 would be 4.242640687 (√18), and we're very careful WHEN dealing with sign ("="), and "2 times of square roots" should be considered as Usage ("SHIFT") sir; Remark: we've already learnt 1=1+1 bugs since 1980s; basicLogic5 has already solved such "bug" (1=1+1) e.g. right side cannot go through left side, if we apply basicLogic5;

I wrote: mochiron of course; be careful with (2 (- , -) keys, 2 Alt keys, 2 Dot keys, 2 Down keys, 2 Enter keys, 2 Left keys, 2 Right keys, 2 Shift keys, 2 Up keys), and I've recommended Time . Space . Action (Oriental Though) should be applied to avoid bugs; Also see: avoiding Earthquake In Japan And Taiwan, And Then, try to realize & understand Nanobot Programming, And Then, realize & understand THAT 2 groups of 3 , and 4 are simplified like 1.384114728; so, you may R&D Anti-Earthquake engineering design model (our earth only), you may also R&D Nanobot Programming (our earth only), ... ;

Fundamental mathematical operations; Algebraic thoughts; Variables; Exponents; Large number vs. Small Number; Operational orders; Distributive property vs. Others; Integer; Coordinated integer graph; Integer's origin; Integer adding; Integer subtracting; Integer multiplying; Integer dividing; Absolute value vs. relative value; Real number; Rational number; Factoring; Squares and Square Roots; Irrational number; Pi is 22/7 [also see: ACT3 108 configuration & C108.GIF], pairs of sticks; Real number; Equation becomes structural by using variable; Solution oriented IQ enhancement by solving basic equations; Equation represents graph; Equivalent object balancing equation of LEFT = RIGHT; Algebra application; Ratio vs. Proportion; Area vs. Perimeter; Problem solving skill enhancement of time, distance, and rate, traditional concept of Time . Space . Action;

Linear equation vs. Linear expression; Slope form; Intercept form; Slope form AND Intercept form; Linear equation represents graph; Structure of Equation vs. System of Equation; Simultaneous equation & its Graph; Inconsistent system; Dependent System; Polynomial; Monomial vs. Polynomial; Simplified polynomial; Polynomial adding; Polynomial subtracting; Polynomial multiplying; Polynomial dividing; Polynomial pattern; Factor; Composite number; Prime number; Square number; Monomial factor vs. Polynomial factor; Diff of 2 square factoring; Quadratic equation, expression, function; Quadratic solution, by factoring, graphing, square rooting, squaring, formulating, ... ;

(

t a k o s h i k i Polynomial, (2+ algebraic terms, 3+ algebraic terms, consisting of several terms), ... ;

t a n k o s h i k i Monomial, (algebraic expression: consisting of 1 term), if (division Method, multiplication Method), And Then, composite quantities, sums of monomials, ... ;

) Also see: Optics;

LOG     LOG     log; Also see: x Computer; y Computer; z Computer;

( zahyo Coordinate, zahyo Coordinate, zahyo Coordinate, zahyo Coordinate, zahyo Coordinate, coordinate, coordinate, coordinate, coordinate, Coordinate) ... ;

	Up

♥ = 1; ♦ = 1;
substitution: ♥ = ♦;
squaring to left and right: (♥^2) = (♦^2);
subtracting each other: (♥^2) - (♦^2) = 0;
multiplying: (♥ * ♥) - (♦ * ♦) = 0;
factoring: (♥ - ♦) * (♥ + ♦) = 0;
dividing by (♥ - ♦): (((♥ - ♦) * (♥ + ♦)) / (♥ - ♦)) = (0 / (♥ - ♦));
simplifying left: (♥ - ♦) / (♥ - ♦) is 1 ?
simplifying right: 0 / (♥ - ♦) is 0 ?
simplify (left, right): 1 * (♥ + ♦) = 0;
anything multiplying by one: (♥ + ♦) = 0;
applying reference to value: 1 + 1 = 0; 2 = 0;
dividing both left and right by two: 1 = 0;
adding one to both sides: 1 + 1 = 1;
because of substitution: ♥ = ♠; ♦ = ♣;
adding one to both sides: 2 + 2 = 2;
adding one to both sides: 3 + 3 = 3;
Therefore, be very careful in programming, regarding algebra;
Therefore, be very careful WHEN dealing with (Ref., Val.);
Therefore, 3 lines should be the most suitable STANDARD, regarding hardware design model;
Therefore, using Katakana keywords (chipset) software design model is the best, and the most reliable;
Therefore, in D A L design model, graphics Definition must be matched;