Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Digging - The PjProblemStrings Sequences

One of the ways humans derive benefits from the earth is to dig it. They dig earth to sow; they dig it to build; they dig it to mine; they dig it to hide valuables and they dig it to bury their loved ones.

(a) The illustrated bulldozer is engaged in simple *digging*. Highlight its *digging*.

(b) Indicate the PjProblem Strings for the highlights. Thus establish the PjProblemStrings Sequences for the *digging*.

Other livings things are also diggers: some rodents dig to hibernate (e.g. the groundhog); bears dig to find food; dogs dig when hot in search of cool space; squirrels dig to hide their food and trees dig in search of water and nutrients.

(c) How does the digging of a tree differ from the digging of the illustrated bulldozer.

(d) Do you agree that walking on sand is digging? If you do, differentiate the digging that results from walking on sand from the digging of the illustrated bulldozer.

(e) Suggest two prerequisites one would need inorder to formulate a mathematical model for the digging of the bulldozer.

(f) Explain the correctness or incorrectness of the following assertion: *every movement on the ground is digging*.

**The strings**: all PjProblems at play.
**The math**: S_{7}P_{3}A_{32} (force - push) and S_{7}P_{3}A_{31} (force -pull) are the PjProblems of interest.

**(a)** : operator of bulldozer positions it some distance from the perimeter of the earth space to be dug.

- Bulldozer's blade is pushed into space to be dug

- Bulldozer's blade scoops some earth

- Bulldozer's blade containing scooped earth is raised.

- Bulldozer moves scooped earth to dump-space.

- Bulldozer's blade returns to space being dug.

This completes the digging cycle which is repeated until the digging is completed. The position of the bulldozer around the space being dug may vary.
**(b)** : - Operator in bulldozer and bulldozer's position - S_{7}P_{1}A_{17} (containership - location)

- Earth space being dug - S_{7}P_{2}A_{21} (identity - physical)

- Bulldozer's blade pushes into earth - S_{7}P_{3}A_{32} (force - push)

- Bulldozer's blade scoops some earth - S_{7}P_{3}A_{31} (force - pull)

- Bulldozer raises scooped earth - S_{7}P_{4}A_{41} (motion - linear)

- Bulldozer moves scooped earth to dump-space - S_{7}P_{4}A_{42} (motion - curvilinear)

- Bulldozer's blade returns to space being dug - S_{7}P_{4}A_{42} then S_{7}P_{4}A_{41}

Thus, the digging PjProblemStrings Sequences are : S_{7}P_{1}A_{17}S_{7}P_{2}A_{21}S_{7}P_{3}A_{32}S_{7}P_{3}A_{31}S_{7}P_{4}A_{41}S_{7}P_{4}A_{42}S_{7}P_{4}A_{42}S_{7}P_{4}A_{41}

Some PjProblem Strings not directly influencing the digging are implied. For example, the equlibrium of the operator and the bulldozer, the grouping/interaction and equilibrium of the earth dumped.
**(c)**: the roots of trees are the diggers. They only push through earth in their search for water and nutrients. They do not pull earth.
**(d)**Yes. It is a *push-digging*.
**(e)**There are several variables in the digging scenario presented.

So, first prerequisute: the variable or variables of interest must be identified.

Second prerequisite: assumptions must be made to reduce the inherent complexities of the model. The assumptions made will depend on the variables of interest.
**(f)**The assertion *every movement on the ground is digging* is correct because all movements on the ground exert *push-forces*. The extent to which the digging impressions are perceived is dependent on the *push-force* and the compactness of the ground.

In general, *all exertions of forces on matter are diggings*. The visibility or invisibility of the *digging impressions* is dependent on the *severity* of the force and the *strength* of the material relative to the force.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings