The Beauty of Maths

Sequential Inputs of numbers with 8
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
......................................

Sequential 1's with 9
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
......................................

Sequential 8's with 9
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
......................................

Numeric Palindrome with 1's
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
......................................

Without 8
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999
......................................

Sequential Inputs of 9
9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001
9999 x 9999 = 99980001
99999 x 99999 = 9999800001
999999 x 999999 = 999998000001
9999999 x 9999999 = 99999980000001
99999999 x 99999999 = 9999999800000001
999999999 x 999999999 = 999999998000000001
......................................

Sequential Inputs of 6
6 x 7 = 42
66 x 67 = 4422
666 x 667 = 444222
6666 x 6667 = 44442222
66666 x 66667 = 4444422222
666666 x 666667 = 444444222222
6666666 x 6666667 = 44444442222222
66666666 x 66666667 = 4444444422222222
666666666 x 666666667 = 444444444222222222
......................................

A Magic Square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. Building on the work of Ahmad ibn ‘Ali al-Buni, in about 1510 Heinrich Cornelius Agrippa wrote De Occulta Philosophia expounding on the magical virtues of seven magical squares of orders 3 to 9, each associated with one of the astrological planets.

Saturn = 15 4 9 2 3 5 7 8 1 6

Jupiter = 34 4 14 15 1 9 7 6 12 5 11 10 8 16 2 3 13

Mars = 65 11 24 7 20 3 4 12 25 8 16 17 5 13 21 9 10 18 1 14 22 23 6 19 2 15

Sol = 111 6 32 3 34 35 1 7 11 27 28 8 30 19 14 16 15 23 24 18 20 22 21 17 13 25 29 10 9 26 12 36 5 33 4 2 31

Venus = 175 22 47 16 41 10 35 4 5 23 48 17 42 11 29 30 6 24 49 18 36 12 13 31 7 25 43 19 37 38 14 32 1 26 44 20 21 39 8 33 2 27 45 46 15 40 9 34 3 28

Mercury = 260 8 58 59 5 4 62 63 1 49 15 14 52 53 11 10 56 41 23 22 44 45 19 18 48 32 34 35 29 28 38 39 25 40 26 27 37 36 30 31 33 17 47 46 20 21 43 42 24 9 55 54 12 13 51 50 16 64 2 3 61 60 6 7 57

Luna = 369 37 78 29 70 21 62 13 54 5 6 38 79 30 71 22 63 14 46 47 7 39 80 31 72 23 55 15 16 48 8 40 81 32 64 24 56 57 17 49 9 41 73 33 65 25 26 58 18 50 1 42 74 34 66 67 27 59 10 51 2 43 75 35 36 68 19 60 11 52 3 44 76 77 28 69 20 61 12 53 4 45

  

The order-4 magic square in Albrecht Dürer's engraving Melencolia I is believed to be the first seen in European art. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares (of the 4 x 4 as well as the four contained 3 x 3 grids). This sum can also be found in the four outer numbers clockwise from the corners (3 + 8 + 14 + 9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle, the two sets of four symmetrical numbers (2 + 8 + 9 + 15 and 3 + 5 + 12 + 14), the sum of the middle two entries of the two outer columns and rows (5 + 9 + 8 + 12 and 3 + 2 + 15 + 14), and in four kite or cross shaped quartets (3 + 5 + 11 + 15, 2 + 10 + 8 + 14, 3 + 9 + 7 + 15, and 2 + 6 + 12 + 14). The two numbers in the middle of the bottom row give the date of the engraving: 1514. The numbers 1 and 4 at either side of the date correspond to, in English, the letters 'A' and 'D' which are the initials of the artist. Dürer's image was distributed widely, and travelled as far away as India, where the Mughal miniaturist Farrukh Beg referenced the work in his 1615 miniature The Old Sufi.

W.D. Gann's Natural Trading Days

From Spring Equinox on March 20th, the Sun has moved 135 degrees of longitude (solar degrees) or 140 calendar days into Tuesday, August 7th. 

 

W.D. Gann always said the year begins on March 21st (not January 1st) and that this was a very important seasonal time. He used geometrical divisions of the solar year (solar degrees of longitude AND calendar days) to ascertain turning points in financial markets. 

Dates 45, 90, 135, 180, 225, 270, and 315 solar degrees from Vernal Equinox (= 0 degrees Aries) are what he called Natural Trading Days.  

Though 15, 22.5 and 45 degrees also may coincide with changes in trend (CITs), Gann stressed the importance of the cardinal points (90 degrees apart). 225 degrees is 0.618 of a solar year.  

 

He also used multiples (squares) of 90 and 144, i.e. 90, 180, 270 etc. and 144, 288, 576, 720. CITs may also occur every 30 degrees (Sun moves into the next sign of the zodiac).

 

Since the Sun moves at different speed, e.g. 45 degrees not always equals 45 calendar days. For calculation an ephemeris is needed (e.g. HERE or HERE). The dates of Vernal Equinox, Summer Solstice, Autumnal Equinox and Winter Solstice slightly change over time (see HERE).

Vernal Equinox in 2012 = March 20th 
Summer Solstice in 2012 = June 20th 
Autumnal Equinox in 2012 = September 22nd 
Winter Solstice in 2012 = December 21st

W.D. Gann's Reading List

In 1946, aged 68, W.D. Gann produced a reading list for his students:

Since Gann’s death in 1955 this reading list has generally been overlooked by Gann enthusiasts because the constituent books have been difficult or expensive to obtain. With the exception of 3 books (see below - highlighted in grey). None of these 3 missing titles is even listed in the Library of Congress Online Catalog. However, copies of all other 76 books from Gann’s recommended reading list are now available free-of-charge and for the benefit of all Gann enthusiasts.

NUMEROLOGY
Numerology by Clifford Cheasley
Philosophy Of Numbers by Mrs L Dow Balliett
Number Vibration In Questions And Answers by Balliett
The Day Of Wisdom According To Number Vibration by Balliett
The Kabala Of Numbers (Part One) by Sepharial
How To Play The Races And Win by Mark Mellen
The Kabala Of Numbers (Part Two) by Sepharial
The Mysteries Of Sound And Number by Sheikh Habeeb Ahmad
Numerology For Everybody by Montrose
The Tarot Of The Bohemians by Papus
The Power Of Numbers by Numero
Numerology Made Plain by Ariel Yvon Taylor

ASTROLOGICAL
Horary Astrology by Robert DeLuce
World Book Of The Ages From Adam To The Millennium by H J Kerns
Raphael’s Pythoness Of The East by Raphael
Raphael’s Book Of Dreams by Raphael
Raphael’s Mundane Astrology - Part 2 - Part 3 by Raphael
Zodiac And Bible by Fannie Muller  Copy Not Yet Available
Mars The War Lord by Alan Leo
Ogilvie’s Astrological Birthday Book by Leo Bernart
Sepharial’s Astrology - Part 2 - by Sepharial
Astrology Explained by Sepharial
Astrology, Its Techniques And Ethics by C Aq Libra
Key To The Bible And Heaven - Part 2 - by Ludwig B Larsen
Science And The Key Of Life - Part 2 - 3 - 4 - 5 - 6 - 7 - by Alvidas
The Wheel Of Life Or Scientific Astrology - Part 2 - 3 - 4 - 5 - by Maurice Wemyss
Raphael’s Book Of Fate by Raphael
Guide To Astrology by Fred White
Law Of Values by Sepharial
The Silver Key by Sepharial
Fortunate Hours by A E Partridge
Directional Astrology by Sepharial
The Stars, How And Where They Influence by L Edward Johndro
The Earth In The Heavens: Ruling Degrees Of Cities by L Edward Johndro
Rectification Of The Horoscope by Robert DeLuce
Astrology For All by Alan Leo
The Secret Of The Ages by Robert Collier
The Science Of Foreknowledge by Sepharial
The Astrological Ready Reckoner And Student’s Assistant - Part 2 - by Sepharial
Your Stars And Destiny by Paul Councel
Manual Of Astrology - Part 2 - 3- 4 - by Sepharial
Textbook Of Astrology - Part 2 - by A J Pearce
The Witness Of The Stars by E W Bullinger
Solar Biology by H E Butler
Cosmic Symbolism by Sepharial
Popular Astronomy by Flammarion And Gore
Eclipses In Theory And Practice by Sepharial
Sun Spots And Weather by W T Foster
Popular Astrology For Everybody by Fredrick Hathaway     Copy Not Yet Available
 
SCIENTIFIC AND MISCELLANEOUS
The Candle Of Vision by “A E”
The Path To Wisdom by Richard Lynch
The Doctor Prescribes Colors by Edward Podolsky
Cosmic Causation In Geophysics by Paul Councel
The Master Key Of Destiny by Gregorius
Evolution And Reincarnation by Essie Ducquan                  Copy Not Yet Available
Miracle Of The Ages by Worth Smith
The Kybalion by The Three Initiates
Sixth And Seventh Books Of Moses
Mysteries Unveiled by William A Redding
Pax Tecum Or Peace And Relaxation Through Technique And Truth by Henry Casper
Faith As A Constructive Force by Swami Paramananda
Oracles Of Nostradamus by Charles A Ward
The Sickle by William W Walter
Lessons In Truth by Emilie Cady
Secret by Wesley W Stout
Open The Door by Wilfred Brandon
The Proofs Of Astral Influence On Man by Paul Choisnard
Spiritual Radio by Archbishop Du Vernet
Yoga System Of Study by Yoga Hari Rama
The Law Of Psychic Phenomena by Thomas Hudson
Power Of Will by Frank Channing Haddock
Oahspe by Dr John Newbrough
Philosophy Of Natural Magic by Henry Cornelius Agrippa
The World Book Of The Ages From Adam To The Millennium by H J Kerns
Bible Mystery And Bible Meaning by Thomas Troward
God-Man: The Word Made Flesh by George W Carey
Tertium Organum by P D Ouspensky
The Chemistry And Wonders Of The Human Body by George W Carey
The World’s Greatest Thought Discovery by Mack Stauffer
The Goal Of Creation - Part 2 - by Edmund Shaftesbury

Sunspots & Stocks

There is a correlation between the Sunspot Cycle and the Stock Market: Since 1933-34 all bull market highs (= start of a bear market) occurred 0-13 months after the peak of the Solar Cycle (List):

• HIGH of Solar Cycle #17 in 4/1937 = bear market starts in the Dow Jones 8/1937 (+4 months)
• HIGH of Solar Cycle #18 in 5/1947 = bear market starts in the Dow Jones 6/1948 (+13 months)
• HIGH of Solar Cycle #19 in 3/1958 = bear market starts in the S&P 500 8/1959 (+6 months)
• HIGH of Solar Cycle #20 in 11/1968 = bear market starts in the S&P 500 12/1968 (+1 month)
• HIGH of Solar Cycle #21 in 12/1979 = bear market starts in the S&P 500 11/1980 (+11 months)
• HIGH of Solar Cycle #22 in 7/1989 = bear market starts in the S&P 500 7/1990 (+12 months)
• HIGH of Solar Cycle #23 in 3/2000 = bear market starts in the S&P 500 3/2000 (+0 month)

In early 1968 the quasi gold standard was more or less abolished, which lead to the inevitable expansion in money supply and inflation. Since that time every solar top made a bubble burst, in 3 of the 4 cases even in the same or following month which is incredibly precise:

• HIGH of Solar Cycle #20 in 11/1968: stock market bubble bursts 12/1968 (the S&P 500 high of late 1968 was only exceeded nominally but not in real terms for decades)
• HIGH of Solar Cycle #21 in 12/1979: commodity bubble bursts 1/1980
• HIGH of Solar Cycle #22 in 7/1989: Japan bubble (stocks & real estate) bursts 12/1989
• HIGH of Solar Cycle #23 in 3/2000: stock market bubble bursts 3/2000

The more sun-spots, the more important for financial markets. The solar super-storms of 1859, 1921 and 1989 went along with inflation peaks (Credits: Manfred Zimmel):

• September 1-2, 1859 (highest inflation 1810-1910).
• May, 1921 (highest inflation 1860-1940).
• 1989 (highest inflation since mid 1960s).

The Peak of the current Sunspot Cycle #24 is projected for spring 2013 (HERE). More related online resources: Solar Cycle Progression - Monthly SSN - Calculated annual average SSN - Solar Cycle start – end months, mid-point

In 1965 Charles J. Collins presented his investigation on "The Effect of Sunspot Activity on the Stock Market" (reprinted in the March 1966 of the 'Cycles' Magazine). His theorem is (briefly stated) the following:

(1) An important market peak has been witnessed or directly anticipated when, in the course of each new sunspot cycle, the yearly mean of observed sunspot numbers has climbed above 50.
(2) In each solar cycle, the largest stock market decline, in terms of percentage drop, comes after the sunspot number, on an annual basis, has climbed above 50.

HERE

HERE

Another pattern of stock market tops about 2.5 years before the Sunspot Peak is based on a 11-year smoothing of the data yielding slightly different highs compared to nominal prices (HERE):

Jeffrey Owen Katz and Donna L. McCormick  developed a profitable Trading System based on Sunspot numbers (HERE & HERE p. 198 ff.):

Like  seasonality  and  lunar phase,  solar  activity  appears  to  have  a  real  influence  on some markets, especially the S&P 500 and Minnesota Wheat. As with lunar cycles, this influence is not sufficiently strong or reliable to be a primary element in a portfolio trading system; however, as a component in a system incorporating other  factors,  or  as  a  system  used  to  trade  specific  markets,  solar  activity  is  worth attention. We personally do not believe solar influences directly determine the market.  We  do  suspect  that  they  act  as  triggers  for  events  that  are  predisposed  to occur, or as synchronizers of already-present market rhythms with similar periodicities. For example, if a market is highly over-valued and unstable, as was the S&P 500 in October 1987, a large solar flare might be sufficient to trigger an already-imminent crash.

The observation that sharp down-turns can occur after solar flares has been supported.

Flares are the most powerful and explosive of all forms of solar eruptions, and the most important in terrestrial effect. Large flares release energy equivalent to the explosion of more than 200 million hydrogen bombs in a few minutes' time, sufficient to meet mankind's energy demands for a 100 million years (HERE - HERE - HERE).

HERE

HERE

HERE

STD Red Week (August 6 - 10)

For previous Short-Term-Delta Red Weeks in the S&P 500 see also HERE

STD Red Weeks oftentimes are trenders from Tuesday open to Friday open.  Monday and Friday often reverse the Tuesday - Thursday trend. This is the STD Red Week's pattern:

Alex Roslin's - COTs Timer (Aug 4)
Smart Money Commercial Hedgers dump S&P 500, COT signal flips to bearish

David Hickson - Hurst cycles (Aug 4)
We are expecting the 80-day cycle peak to form in the US markets soon, after which there will be a fall into the 80-day cycle trough which is expected in late August.
[Hurst triad] lines are presently projecting a target for the peak of 1400-1420.

Mike Burk - Seasonality (Aug 4)
As measured by the S&P 500 August has been, by far, the strongest month of the 4th year of the Presidential Cycle. I expect the major averages to be higher on Friday August 10 than they were on Friday August 3.

www.chartsedge.com

www.alphee.com

www.astrocycle.net

The Nasdaq 100 ETF (QQQ) broke above resistance from the July highs
and remains in an uptrend, but a spinning top formed on Friday.
These candlesticks show indecision and the prior two foreshadowed
pullbacks within the uptrend [Arthur Hill]