Doc Benton's Academy for Mathematical, Astrological, and Kabbalistic Wizards!


Maple Syrup ~ LiveMath



Welcome to "Doc Benton's Academy for Mathematical, Astrological, and Kabbalistic Wizards!" I have been retired for an indeterminate amount of time, and this site, like a freeway in Texas, will be under construction forever. Nonetheless, below is what I have accomplished so far in my quest to create a very brief, 900-page introduction to group theory that either an intelligent high school student or a caveman working for GEICO could benefit from. And as the erroneous perception of linear time goes by, I will clean up and simplify the text as much as possible in order to make everything perfectly clear and unambiguous. Enjoy!

A Child's Garden of Groups

An introduction to the mathematical theory of
groups for young and old!
Subgroups, Cosets and Equivalence Relations! Dihedral Groups, Symmetric Groups, Alternating
Groups, Direct Products, and Semidirect Products!
The Structure of Groups of Order 1 through 10 Visual Representations of Groups Frieze Groups, Wallpaper Groups, and Free
Range Symmetry
Matrix Groups Deep Inside Rubik’s Cube Proving Theorems! Isomorphisms, Homomorphisms, and Theorems

Doc Benton's Journal


The Best of Doc Benton

Einstein's Theory of Special Relativity E=mc-squared in One Page! Pi Day! The Pythagorean Theorem How to factor trinomials - proof Reflections on Educational Practices in
Rabbbinic Literature
Best Practices Algebraic Models for Constructivist Theories of Perception Forbidden Secrets of Multivariable Calculus Multivariable Calculus Software Tools
Greatest Common Divisors The Torah of Pi Infinity The Book of the Assembler Kabbalah Class The Unreality of Reality Running and Returning In the Beginning ... Righteousness and the Tabernacle Doc Benton and the Case of the Missing God (For Mad Men Only)
One Page Torah The Shape of Things to Come Notes on the Essence of Jewish Mysticism Q-Astrology: Quaint, Quantitative, Quotient, Questing, Questioning The Leviticus Cookbook Jewish Wisdom Quotes Aba

General Math

Statistics Business Calculus Advanced Business Math Multivariable Calculus Factoring Examples How to Solve a Cubic Equation How to Solve a Quartic Equation Doc Benton's Video Ranch Math Song Final Talk


Statistics Examples

Statistics and Austerity Economics

Statistics and Gun Laws

Statistics and the Media

Statistics and Biased Studies

Statistics and Reporting

Statistics and Measurement Error

Statistics and Causation

Statistics and Climate Change

Statistics and Graphs

Statistics and Demographic Changes

Statistics and Early Death

Statistics and Biased Interpretations

Statistics and Biased Samples

Statistics and Not So Good Graphs

Sampling Error


Differential Equations

What is a Differential Equation? Separable Differential Equations Exact Differential Equations Integrating Factors Constant Coefficients Springs The Incredible Harmonic Oscillator! Laplace Transforms Doc Benton's Favorite Laplace Transforms Gamma Function


Astrology 2022

The 2022 Jupiter/Neptune Conjunction (pdf) The 2022 Jupiter/Neptune Conjunction (slideshow) 2022 Aspects that I Worry About Russia, Ukraine, USA My Predictions for 2022 My Predictions for 2022 with notes Summary of My Weather Report for 2022 Transits for Russia and Ukraine  Election Day 2022 Something Good
The Best Day of the Decade The Summer of Love The Summer of Nonbinary Love & Cannabis Death and Transformation A Pleasant Summer American Fanaticism American Exceptionalism Jupiter conjunct Neptune in Pisces - 1856 Jupiter conjunct Neptune in Pisces - 2022 Civil War 1861
Civil War 2026 Mars Goes Retrograde USA July 2nd Libra Rising Chart USA July 4th Gemini Rising Chart USA July 4th Sagittarius Rising Chart USA Articles of Confederation USA Constitution Transits for Joe Biden 2022 Astrology Podcast for the Year Ahead Themes for 2022 (Pam Gregory)
Global 2022 Jupiter/Neptune Conunction (Pam Gregory) Pluto in 2022 Rick Levine's Astrology Forecast for January 2022 New Moon in Capricorn 2nd January 2022 Full Moon in Cancer 17th January 2022  February 2022 Astrology Podcast Rick Levine's Astrology Forecast for February 2022 New Moon in Aqauarius 1st February 2022 Full Moon in Leo 16th February 2022
February 2022 Vladimir Putin March 5 2022 Mars/Venus Conjuncton March 6 2022 Spring Equinox March 20 2022 Joe Biden March 25 2022 Ukraine Hard Transits Russia Hard Transits Putin Hard Transits Biden Hard Transits America Hard Transits
Zelenskyy Hard Transits China Hard Transts Timeline March 12 through April 30 Barbault Planetary Cycle Index            



Graphic Ephemeris 2022 Graphic Ephemeris USA 2022 Graphic Ephemeris Russia 2022 Graphic Ephemeris Ukraine 2022 Graphic Ephemeris China 2022 Graphic Ephemeris Iran 2022 Graphic Ephemeris Me 2022 Graphic Ephemeris Susan 2022 USA Planetary Stations 2022 My Planetary Stations 2022
Ephemeris February 2022 Ephemeris March 2022 Ephemeris April 2022 Ephemeris May 2022 Graphic Ephemeris Putin 2022 Graphic Ephemeris Zelenskyy 2022 Graphic Ephemerics Biden 2022 Graphic Heliocentric Ephemeris 2022 Graphic Ephemeris March 2022 Graphic Ephemeris 1st Quarter of Moon
Graphic Ephemeris Heliocentric 30 Years Graphic Ephemeris Heliocentric 20 Years Graphic Ephemeris Heliocentric 10 Years Graphic Ephemeris Heliocentric 1 Year Graphic Ephemeris Heliocentric 1 Month Graphic Ephemeris Heliocentric 1 Week Graphic Ephemeris Trump 2022 Graphic Ephemeris Geocentric 1 Month Graphic Ephemeris Geocentric 1 Week  
September Ephemeris October Ephemeris November Ephemeris December Ephemeris January Ephemeris February Ephemeris March Ephemeris      


Equinoxes and Solstices

Spring Equinox 2022 Summer Solstice 2022 Fall Equinox 2022 Winter Solstice 2022
Spring Equinox 2022 (heliocentric) Summer Solstice 2022 (heliocentric) Fall Equinox 2022 (heliocentric) Winter Solstice 2022 (heliocentric)



New Moon January 2 2022 Full Moon January 17 2022 New Moon January 31 2022 Full Moon February 16 2022 New Moon March 2 2022 Full Moon March 18 2022 New Moon March 31 2022 Full Moon April 16 2022 Solar Eclpse April 30 2022 Lunar Eclipse May 15 2022 New Moon May 30 2022 Full Moon June 14 2022
New Moon June 28 2022 Full Moon July 13 2022 New Moon July 28 2022 Full Moon August 11 2022 New Moon August 27 2022 Full Moon September 10 2022 New Moon September 25 2022 Full Moon October 9 2022 Solar Eclipse October 25 2022 Lunar Eclipse November 8, 2022 New Moon November 23 2022 Full Moon December 4 2022
New Moon December 23 2022 Heliocentric New Moon 3-2-2022 Heliocentric Full Moon 3-18-2022 Heliocentric New Moon 3-31-2022 Heliocentric Full Moon 4-16-2022 Heliocentric Solar Eclipse 4-30-2022 Heliocentric Lunar Eclipse 5-15-2022  


Monthly Transits

New Moon 1st Quarter Moon Full Moon 3rd Quarter Moon
My New Moon Biwheel My 1st Quarter Biwheel My Full Moon Biwheel My 3rd Quarter Biwheel
Susan's New Moon Biwheel Susan's 1st Quarter Biwheel Susan's Full Moon Biwheel Susan's 3rd Quarter Biwheel
New Moon Transits 1st Quarter Transits Full Moon Transits 3rd Quarter Transits
Graphic New Moon Transits Graphic 1st Quarter Transits Graphic Full Moon Transits Graphic 3rd Quarter Transits
My New Moon Transits My 1st Quarter Transits My Full Moon Transits My 3rd Quarter Transits
Susan's New Moon Transits Susan's 1st Quarter Transits Susan's Full Moon Transits Susan's 3rd Quarter Transits
Transit Grid Transit Scan Transit Interpretation Transit EXL
My Transit Grid My Transit Scan My Transit Interpretation My Transit EXL
Susan's Transit Grid Susan's Transit Scan Susan'sTransit Interpretation Susan's Transit EXL
USA Transit Interpretation USA Transit EXL Russia Transit Interpretation Russia Transit EXL
Ukraine Transit Interpretation Uraine Transit EXL Biden Transit Interpretation Biden Transit EXL
Putin Transit Interpretation Putin Transit EXL Trump Transit Interpretation Trump Transit EXL
Transit Grid Heliocentric Transit EXL Heliocentric My Outer EXL Susan's Outer EXL
My Midpoint Transits My Midpoint Chart My Chart My Aspects
Susan's Midpoint Transits Susan's Midpoint Chart Susan's Chart Susan's Aspects
Trump Midpoint Transits Trump Midpoint Chart Donald Trump Sign Changes
Putin Midpoint Transits Putin Midpoint Chart Vladimir Putin Ingresses
Biden Midpoint Transits Biden Midpoint Chart Joe Biden Stations
USA July 2 Midpoint Transits USA July 2 Midpoint Chart USA July 2 Russia Midpoint Chart
USA July 4 Midpoint Transits USA July 4 Midpoint Chart USA July 4 Ukraine Midpoint Chart
My 4th Harmonics My 6th Harmonics My 8th Harmonics My 12th Harmonics
Mars My 4th Harmonics Mars My 6th Harmonics Mars My 8th Harmonics Mars My 12th Harmonics
Susan's 4th Harmonics Susan's 6th Harmonics Susan's 8th Harmonics Susan's 12th Harmonics
Mars Susan's 4th Harmonics Mars Susan's 6th Harmonics Mars Susan's 8th Harmonics Mars Susan's 12th Harmonics
Putin 4th Harmonics Putin 6th Harmonics Putin 8th Harmonics Putin 12th Harmonics
Mars Putin 4th Harmonics Mars Putin 6th Harmonics Mars Putin 8th Harmonics Mars Putin 12th Harmonics
Putin 4th Harmonics 2023 Putin 6th Harmonics 2023 Putin 8th Harmonics 2023 Putin 12th Harmonics 2023
Mars Putin 4th Harmonics 2023 Mars Putin 6th Harmonics 2023 Mars Putin 8th Harmonics 2023 Mars Putin 12th Harmonics 2023
Trump 4th Harmonics Trump 6th Harmonics Trump 8th Harmonics Trump 12th Harmonics
Mars Trump 4th Harmonics Mars Trump 6th Harmonics Mars Trump 8th Harmonics Mars Trump 12th Harmonics
Trump 4th Harmonics 2023 Trump 6th Harmonics 2023 Trump 8th Harmonics 2023 Trump 12th Harmonics 2023
Mars Trump 4th Harmonics 2023 Mars Trump 6th Harmonics 2023 Mars Trump 8th Harmonics 2023 Mars Trump 12th Harmonics 2023

Daily Chart



Geocentric Aspects

Heliocentric Aspects

Solar Weather





International Society for Astrological Research Aquarius Papers Astrology Arizona The Historical Ephemeris Astrology Land Spirit Grooves Cosmic Patterns Matrix Software Solar Fire Changing of the Gods
The First 32 Harmonics Capricorn Astrology Research Astrodienst Chris Brennan Astrology Steve Judd Astrology Astrotheme The Mountain Astrologer AstroApp Luna Astrology Using the Vedic saptamsa &
navamsa charts
in western tropical astrology
Astrology cafe Astrology King The Astrology Podcast The Hellenistic Astrology Website Seven Stars Astrology  Astro-seek https://zodiacalreleasing.net/ http://nataltransits.com/timelord.html Raymond Merriman Astrodatabank
http://mundaneastrologers.com/ Historical Astrology Astrology Critics Gravimetric Tides Kapiel Raal Vedic Astrology Sam Geppi Vedic Astrology The Astrological Association Time_Dependent_Nuclear_Decay_Parameters.pdf Astrological Research Centre   

Netflix Prime Video Hulu Disney Plus HBO Max Roku Youtube TV Youtube Washington Post Amazon
Pandora Sefaria Pubmed GoDaddy Facebook Bank of America Fidelity USA Facts Census BLS
Data United Nations Google Arizona State Retirement System USAA Mr. Cooper Bank of America Associated Press Reuters News Zippy


Astrology Videos

David Cochrane Astrology Rick Levine Astrology Steve Judd Astrology The Astrology Podcast Pam Gregory Astrology Bracha Goldsmith Astrology Elizabeth Peru Astrology Kapiel Raaj Vedic Astrology Sam Geppi Vedic Astrology

Mundane Astrology

USA July 2, 1776 Russia China Ukraine United Kingdom Israel Iran Germany Canada Mexico
Neptune/Jupiter 1856 Pluto/Neptune 1892 Chiron/Saturn 1966 Pluto/Uranus 1966 Neptune/Saturn 1989 Neptune/Uranus 1993 Pluto/Chiron 1999 Chiron/Jupiter 2009 Neptune/Jupiter 2009 Neptune/Chiron 2010
Pluto/Saturn 2020 Pluto/Jupiter 2020 Saturn/Jupiter 2020 Neptune/Jupiter 2022 Joe Biden Vladimir Putin Donald Trump Current Transits Election Day 2022 Something Good
The Best Day of the Decade The Summer of Love The Summer of Nonbinary Love & Cannabis Jupiter conjunct Neptune in Pisces - USA 1856 Jupiter conjunct Neptune in Pisces - USA 2022 Civil War 1861 Civil War 2026 September 11 Attack Transits 3-28-2022 Venus conjunct Saturn Transits 3-31-2022 New Moon
Transits 3-31-2022 Moscow, Russia Transits 3-31-2022 Berlin, Germany Transits 4-2-2022 Sun/Mercury/Chiron conjunction Transits 4-2-2022 Sun/Mercury/Chiron conjunction - Los Angeles, California Transits 4-4-2022 Saturn conjunct Mars Transits 4-4-2022 Saturn conjunct Mars - Washington, D.C. Transits 4-4-2022 Saturn conjunct Mars - Kiev, Ukraine Transits 4-4-2022 Saturn conjunct Mars - Moscow, Russia Transits 4-4-2022 - Vladimir Putin Transits 4-5-2022 Mars square Lunar Nodes - New York, New York
Transits 4-8-2022 1st Quarter Transits 4-8-2022 1st Quarter - Moscow, Russia Transits 4-8-2022 1st Quarter - Limoges, France Transits 4-9-2022 Transits 4-11-2022 Saturn square Lunar Nodes Transits 4-12-2022 Jupiter conjunct Neptune Transits 4-12-2022 - San Francisco, United States Transits 4-12-2022 - Stockholm, Sweden Transits 4-16-2022 Full Moon Transits 4-16-2022 - Scottsdale, Arizona
Transits 4-23-2022 - The end of "Kala Sarpa Yoga" as Mercury reaches the other side of a Lunar Node Transits 4-27-2022 Venus conjunct Neptune Transits 4-29-2022 Pluto retrograde Transits 4-30-2022 Solar Eclipse Transits 4-30-2022 Solar Eclipse - Los Angeles, California Transits 4-30-2022 Solar Eclipse - Washington DC, United States Putin Mars square Moon 4-18-2022 Putin Uranus inconjunct Sun 4-19-2022 Putin Jupiter square Mars 4-23-2022 Putin Chiron opposition Sun 4-29-2022
American Transits Expected and Observed for 2022 Expected and Observed Video (Part 1) Expected and Observed Video (Part 2) Expected and Observed Video (Part 3) Expected and Observed Video (Part 4) Is America Headed Toward Another Civil War? (Video) Is America Headed Toward Another Civil War? (Video) Changing Times - The 2020s and Beyond (Video) USA July 2, 1776, 0-Aries
Joe Biden Joe Biden 4th Harmonic USA 4th USA 6th USA 8th USA 12th Mars USA 4th Mars USA 6th 4th Harmonic Transits 6th Harmonic Transits
World 4th World 6th World 8th World 12th Mars World 4th Mars World 6th Mars World 8th Mars World 12th Sign Changes Ingresses
USA 4th 2023 USA 6th 2023 USA 8th 2023 USA 12th 2023 Mars USA 4th 2023 Mars USA 6th 2023 Mars USA 8th 2023 Mars USA 12th 2023 USA July 2, 1776 Stations
Russia 4th 2023 Russia 6th 2023 Russia 8th 2023 Russia 12th 2023 Mars Russia 4th 2023 Mars Russia 6th 2023 Mars Russia 8th 2023 Mars Russia 12th 2023 Russia USA Libra Saturn/Chiron Arc Transform
2023 The Next Three Months in America                


Astrological Calendars

My Calendar 2022 Susan's Calendar 2022 USA Calendar 2022 Biden Calendar 2022 Putin Calendar 2022 Russia Calendar 2022 Ukraine Calendar 2022      

My Natal Charts

Regiomontanus Whole Midpoints Placidus Porphyry Koch Aries Equal Campanus Medieval 
Arabic Parts Hellenistic Aspects Stars Sidereal Baytown Houston Austin Alvin Scottsdale
San Diego All House Cusps Vedic Jerusalem            


My Returns

Lunar Return 9-15-2022 Lunar Return Biwheel 9-15-2022 Lunar Return 10-12-2022 Lunar Return Biwheel 10-12-2022 Lunar Return 11-9-2022 Lunar Return Biwheel 11-9-2022 My Chart
Solar Return 5-23-2022 Solar Return Biwheel 5-23-2022 Solar Return 5-23-2023 Solar Return Biwheel 5-23-2023 My 12th Harmonic Chart My 17th Harmonic Chart My Aspects


Susan's Returns

Susan's Lunar Return 9-11-2022 Susan's Lunar Return Biwheel 9-11-2022 Susan's Lunar Return 10-8-2022 Susan's Lunar Return Biwheel 10-8-2022 Susan's Lunar Return 11-5-2022 Susan's Lunar Return Biwheel 11-5-2022 Susan's Chart
Susan's Solar Return 8-18-2021 Susan's Solar Return Biwheel 8-18-2021 Susan's Solar Return 8-18-2022 Susan's Solar Return Biwheel 8-18-2022     Susan's Aspects


My Arc Transforms

Mercury/Uranus Uranus/Chiron Saturn/Neptune Pluto/Ascendant Saturn/Venus Uranus/Ascendant Jupiter/Neptune
Saturn/Ascendant Venus/Pluto Pluto/Neptune Uranus/Pluto Saturn/Pluto  


Susan's Arc Transforms

Mars/Pluto Moon/Saturn Jupiter/Neptune Saturn/Ascendant Saturn/Pluto


My Harmonic Charts

1st Harmonic 2nd Harmonic 3rd Harmonic 4th Harmonic 5th Harmonic 6th Harmonic 7th Harmonic
8th Harmonic 9th Harmonic 10th Harmonic 11th Harmonic 12th Harmonic 17th Harmonic 24th Harmonic
32nd Harmonic 36th Harmonic 102nd Harmonic 420th Harmonic 420th Heliocentric Harmonic  


Susan's Harmonic Charts

1st Harmonic 2nd Harmonic 3rd Harmonic 4th Harmonic 5th Harmonic 6th Harmonic 7th Harmonic
8th Harmonic 9th Harmonic 10th Harmonic 11th Harmonic 12th Harmonic 16th Harmonic 24th Harmonic
32th Harmonic 36th Harmonic 96th Harmonic 192nd Harmonic 286th Harmonic


Hellenistic Astrology

My Whole Sign Chart My Annual Profections My Current Zodiacal Releasing - (spirit) My Zodiacal Releasing (2-levels) My Zodiacal Release (3-levels, part 1) My Zodiacal Release (3-levels, part 2) My Zodiacal 5 years (4-levels)
Susan's Whole Sign Chart Susan's Annual Profections Susan's Current Zodiacal Releasing (spirit) Susan's Zodiacal Releasing (2-levels) Susan's Zodiacal Release (3-levels, part 1) Susan's Zodiacal Release (3-levels, part 2) Susan's Zodiacal 5 years (4-levels)


Phase Angle Charts

My Solar Phase Angle Chart My Lunar Phase Angle Chart My Mercury Phase Angle Chart My Venus Phase Angle Chart My Mars Phase Angle Chart My Jupiter Phase Angle Chart        


Heliocentric Charts

My Helocentric Chart Susan's Heliocentric Chart Me/Susan Heliocentric Composite Geocentric Aspects Versus Heliocentric Aspects My Heliocentric Biwheel My Heliocentric Transits Susan's Heliocentric Biwheel Susan's Heliocentric Transits Heliocentric Transits Heliocentric Graphic Ephemeris
Heliocentric USA July 2 1776 Heliocentric USA July 4 1776                


Planetry Patterns

Marc Edmund Jones Planetary Patterns Startypes Patterns Startypes Book and Ephemeris


Q-Astrology: Quaint (traditional), Quantitative, Quotient, Questing, Questioning

The Cycle of Becoming, Quotient Structures, Harmonic Charts, and Arc Transforms Astrology and Fractals Arc Transform Charts - John Townley My 17th Harmonic Using Arc Transforms to Understand Transits The Mars/Neptune Arc Transform in the USA Chart Mathematical Models for Aspects Quotient Structures and Graphic Ephemerides Quotient Structures and Harmonic Astrology Quotient Structures and Midpoints
Quotient Structures and Composite Charts Quotient Structures and the Sabian Symbols Quotient Structures and Enlightenment Orbs in Harmonic Charts The Cycle of Becoming Uranus-Chiron Arc Transform Uranus-Ascendant Arc Transform Astrology and Complex Numbers

Q-Astrology: Quaint, Quantitative, Quotient, Questing, and Questioning