Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
PjProblemStrings Sequences are the work-horses of dynamic spaces. The primary types are as follows:
(1) Stand-alone PjProblemStrings Sequences
(2) Queueing PjProblemStrings Sequences
(3) Colliding PjProblemStrings Sequences
(4) Displacement PjProblemStrings Sequences
(5) Overlapping PjProblemStrings Sequences
(6) Hovering PjProblemStrings Sequences
(7) Linked PjProblemStrings Sequences
(a) Give at least one example for each of the seven types
of PjProblemStrings Sequences.
(b) Interprete Newton's first and third laws of motion in the context of PjProblemStrings Sequences.
S7P3A3k (force -k =1, 2), S7P4A4k (motion- k =1, 2, 3,4).
All Pj Problems are at play. However, Pj Problems of Interest are of types force and motion.
(1) Stand-alone PjProblemStrings Sequences: examples are a crane offloading containers one at a time; walking; running; driving a car; flying an airplane. In essence all solo motions are of this type.
The remaining six types are different groupings/interactions of stand-alone PjProblemStrings Sequences.
(2) Queueing PjProblemStrings Sequences: examples are, customers queueing in front of the service counter of a service company; cars queueing at a traffic light, marching in single file, etc.
(3) Colliding PjProblemStrings Sequences: examples are, two lovers kissing; a sperm fertilizing and ovum; two or more cars colliding; a missile hitting an aircraft; a batter hitting the baseball thrown by a pitcher; kinetic collisions when heat is applied to matter, etc.
(4) Displacement (or Replacement) PjProblemStrings Sequences: examples are, drinking with a straw (suction - air moves, liquid replaces); convection flow (warm air rises, cold air sinks).
(5) Overlapping PjProblemStrings Sequences: covalent bonding (atomic orbitals overlap to form molecular orbitals).
(6) Hovering PjProblemStrings Sequences: examples are, a cop helicopter trailing a suspect, a skateboarder's jump; a stuntman's jump. In this type, the hovering PjProblemStrings Sequence hovers above another PjProblemStrings Sequence sequence.
(7) Linked PjProblemStrings Sequences: examples are, a moving train; a tow truck towing a vehicle.
(bi) Newton's First Law: an object at rest will remain at rest and an object in motion will remain in motion at constant velocity unless acted upon by an unbalanced force.
In the context of PjProblemStrings Sequences, colliding PjProblemStrings Sequences are needed to overcome the inertia of an object at rest and an object in motion at constant velocity. A stand-alone PjProblemString Sequence is created in the former scenario and the stand-alone PjProblemString Sequence in the latter scenario is change to an accelerating sequence after collision. In the case of an automobile, the collision occurs between the foot and the accelerator pedal.
(bii) Newton's Third Law: for every action, there is an equal and opposite reaction. In other words, all forces come in pairs.
Hence PjProblemStrings Sequences are motions sandwiched between two forces. The first force is a resultant force (action - reaction) causing motion. The second force opposes motion. Motion continues until the resultant force equals zero.
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 = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
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
Derivation Of Heat Equation For A One-Dimensional Heat Flow
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.
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