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

1895 - 1911 Sixteen Years Of Great Discoveries

The human story is primarily about survival and discoveries. Many persons young and old from various parts of the world have been contributors to the important story of great human discoveries. The discoveries indicated in *1895-1911. 16 years of open brains* are important snapshots from the human *Knowledge Continuum*.

(a) Indicate the discoverers and primary underlying concepts of the discoveries highlighted in *1895-1911. 16 years of open brains*.

(b) What is meant by *open brain* and *stringed brain*?

**The strings**:

S_{7}P_{2}A_{22} (Identity - Chemical Properties).
**The math**:

Pj Problem of Interest is of type *identity* (chemical properties). Both physical and chemical identities are at play here. However, the *identity* of the chemical properties of these discoveries are dominant. Hence, the Pj Problem of Interest is of type *identity - chemical properties*

(a)

(i) **1895: X-rays were discovered**. Wilhelm Konrad Rontgen (1845-1923) is credited with the discovery. The underlying concept is that light invisible to the unaided eye, could penerate matter that is impervious to ordinary light and could produce fluorescence in various substances.

(ii) **1896: radioactivity was discovered**. Henri Becquerel (1852-1908) is credited with the discovery. The underlying concept is that energy and matter can be released as a result of changes in the nucleus of an atom. Becquerel used Uranium in his experiment. In the same year, Marie Sklodowska Curie (1867-1934) in association with her husband Pierre Curie (1859-1906) showed that some other substances other than uranium are radioactive. The two substances they found to be radioactive they named polonium and radium.

(iii) **1897: the electron was discovered**. G. Johnstone Stoney (1826-1911) is credited with being the first to suggest (in 1874) the existence of charged discrete units of electricity associated with atoms. In 1891 Stoney suggested the name *electron* for this discrete unit of electricity. However, Joseph John Thomson (1856-1940) is credited with the discovery of the actual existence of the electron and some of its properties. Electrons are central to all interactions in the physical universe.

(iv) **1899: α radiation β radiation were discovered**. Ernest Rutherford (1871-1937) is credited with the discovery. Paul Villard (1860-1934) discovered Gamma (γ) radiation, shortly after. These discoveries identified the nature of the radiation from uranium. Rutherford showed that α rays are positive parts of helium atoms moving at high speed. β rays are electrons moving at high speed. γ rays are short wavelength rays similar to visible light.

(v) **1900: Quantum Theory was discovered**. Max Planck (1858-1947) is credited with the discovery. Over the years, several great individuals set the stage for its heralding: Isaac Newton's wave theory of light and the light particles he called *corpuscles*; the wave theory of light of Christian Huygens (1629-1695), Augustine Jean Fresnel (1788-1827) and Thomas Young (1773-1829); James Clerk Maxwell's wave equation and the confirmatory experiment by Heinrich Hertz (1857-1894). The underlying concept is that energy is transfered in discrete units called *quanta*.

(vi) **1905: photon (light quanta) was discovered**. Albert Einstein is credited with this discovery. The discovery established the particle nature of light that arose from the theory of photoelectric effect. Einstein established the *photoelectric equation* which states that the energy of the light quantum is the sum of the energy required to remove the electron from the metal and the kinetic energy imparted to the electron.

(vii) **1911: atomic nuclei were discovered**. Ernest Rutherford (1871-1937) is credited with the discovery. Rutherford's interpretation in 1911 of his experiment on the scattering of alpha rays by a thin sheet of mica and a similar experiment by H. Geiger and E. Marsden on the scattering of alpha rays by gold foil, established the discovery. Rutherford's interpretation posited that the results of the experiments showed that most of the mass of an atom is concentrated in a single particle that is very small relative to the atom itself. This particle we now know as the nucleus of an atom.
**1895 -1911**. 16 years in which open brains established discoveries that were critical intellectual prerequisites for the actualization of the quantum intellectual leap of homo sapiens sapiens.

(b) An *open brain* is a brain from which flow new discoveries. A *stringed brain* is a brain able to make unified sense of all the discoveries. An *open-stringed brain* is a brain that is both *open* and *stringed*.

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