ODDWHEEL: Magic Squares, Squares of Squares and Interleaved Sequences

Citric and Isocitric/Alloisocitric acids Using HOMO-LUMO Interactions

Picture of a wheel on stairs

HOME to THE WHEEL, LOUBÈRE, MÉZIRIAC, KNIGHT, de la HIRE, Cross and Mask METHODS


Table of Contents 0A
  
Citric Acid Section
  
1. Synthesis of citric acid, HOMO-LUMO interaction of allyl anion of aconitate with Hydroxide
2. Synthesis of Isocitric acids, HOMO-LUMO interaction of ethene group of (E) and (Z) aconitic acid to generate Isocitrate and Alloisocitrate
3. Dehydration of Citric Acid
  


Page 1 Square of Squares - Imaginary Numbers and Tuple Conversion Table of Contents 0B
  
Page 1 Wheel Section - Transpose and Border Squares Table of Contents IA and IB
  
Page 2 Regular and Complex number squares Table of Contents II
  
Page 2 Interleaved Sequences and Bremner Type Squares Table of Contents II
  
Page 2 Mask, Cross and LaHire Type Squares Table of Contents III
  
Page 2 Loubère, Méziriac and Knight Type Squares Table of Contents IV
  
Table of Contents 0B
  
Imaginary and Square of Squares Section
  
1. Use of Imaginary Numbers for Square of Squares (Part IA)
2. Table of Tuples Using Imaginary Numbers for Square of Squares (Part IIA)
3. Table of Tuples and Use of Magic Ratio (R) for Tuple Conversion (Part IB)
4. Table of Tuples for Square of Squares (Part IC)
5. Table of Tuples for Square of Squares (Part IIC)
6. Table of Tuples for Square of Squares (Part IIIC)
7. Table of Tuples for Square of Squares (Part ID)
8. Table of Tuples for Square of Squares (Part IE)
9. Conversion of Tuples to Higher Series of Tuples (Part IF)
10. Conversion of Tuples to Higher Series of Tuples (Part IIF)
11. Conversion of Tuples to Higher Series of Tuples (Part IIIF)
12. Geometric Progression of Tuple Numbers to Generate New Sequences (Part IVF)
13. Geometric Progression and Recursive Methods to Generate New Sequences (Part VF)
14. Recursion Methods to Generate New Integer Sequences (Part VIF)
15. Squares of Seven Squares using Imaginary Numbers (Part IG)


Table of Contents IA
  
Wheel Section
  
1. Introduction and Discussion
2. Magic Square Wheel Method A-1:Variant 1
3. Magic Square Wheel Method A-1:Variant 2
4. Magic Square Wheel Method A-1:Variant 2 7x7
5. Magic Square Wheel Method A-1:a 9x9 Variant
6. Magic Square Wheel Method A-2 Template Inversion
7. Method B Wheel Expansion
8. Method C: Expansion of Wheel Squares Part IIIB
9. Method C: Continuation of Part IIIB
10. Method D: Wheel Spoke/Anti-Spoke Method Part IV
11. New 7x7 Magic Squares Wheel Method Part I (2015)
12. New 7x7 Magic Squares Wheel Method Part II (2015)
13. New 9x9 Magic Squares Wheel Method Part III (2015)
14. New 9x9 Magic Squares Wheel Method Part IV (2015)
15. New 9x9 Magic Squares Wheel Method Part V (2015)
16. New 7x7 Magic Squares Wheel Method Part VI (2015)
17. New 9x9 Magic Squares Wheel Method Part VII (2015)
18. New 7x7 Magic Squares Wheel Method Part VIII (2015)
19. New 9x9 Magic Squares Wheel Method Part IX (2015)
20. New 9x9 Border Magic Squares Wheel Method Part X1 (2015)
21. New 9x9 Border Magic Squares Wheel Method Part X2 (2015)
22. New 11x11 Border Magic Squares Wheel Method Part X3 (2015)
23. New 11x11 Border Magic Squares Wheel Method Part X4 (2015)


Table of Contents IB-New Items (Transpose Wheel and Wheel border Squares)
  
1. New Wheel Transposed magic border squares
2. New Magic Square Wheel Methods- Spoke Shift
3. New Sequences from Magic Square Diagonals (Part A)   
4. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part A
5. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part B
6. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part C
7. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part D
8. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Variant
9. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part E
10. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part F
11. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares Part G
12. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A)      
13. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part B)  
14. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part C)  
15. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part D)  
16. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (PartE)  
17. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part F)  
18. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part G)  
19. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part A)  
20. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part B)  
21. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part C)  
22. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part D)  
23. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part E)  
  
Table of Contents-New Items 2014 Section IIA
  
1. New Sequence from Magic Square Diagonals (Part B)   
2. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part A1)
3. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part A2)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A3)
5. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A4)
6. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part A5)
7. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part A6)
  
1. A Known Sequence from Magic Square Diagonals (Part C)  
2. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part B1)
3. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part B2)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part B3)
5. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part B4)
6. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part B5)
7. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part B6)
  
1. A Known Sequence from Magic Square Diagonals (Part D)  
2. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part C1)
3. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part C2)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part C3)
5. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part C4)
6. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part C5)
7. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part C6)
8. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part C7)
9. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part C8)
10. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part C9)
11. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part C10)
  
1. A Known Sequence from Magic Square Diagonals (Part E)  
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part D1)
3. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part D2)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part D3)
5. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part D4)
6. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part D5)
7. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part D6)
8. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part D7)
9. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part D8)
  
1. A New Sequence from Magic Square Diagonals (Part F)  
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part H1)
3. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part H2)
4. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part H3)
5. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part H4)
  
Section IIB
Novel New Shift Wheel and Transposed Shift Wheel Magic Border Squares
1. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A1)
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A2)
3. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A3)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part A4)
5. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part A5)
6. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part A6)
7. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part A7)
8. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part A8)
  
Section IIC
Novel New Shift Wheel and Central Column Transposed Shift Wheel Magic Border Squares
Unmodified Central Column
1. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part M1)
2. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part M2)
3. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part M3)
4. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part M4)
5. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part M5)
6. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part M6)
  
Section IID
Novel New Shift Wheel and Central Column Transposed Shift Wheel Magic Border Squares
Modified Normal Central Column
1. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part N1)
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part N2)
3. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part N3)
4. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part N4)
5. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part N5)
6. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part N6)
7. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part N7)
8. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part N8)
9. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part N9)
10. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part N10)
  
Section IIE
Novel New Shift Wheel and Central Column Transposed Shift Wheel Magic Border Squares
Modified Non-Normal Central Column (Type A)
1. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part P1)
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part P2)
3. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part P3)
4. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part P4)
  
Section IIF
Novel New Shift Wheel and Central Column Transposed Shift Wheel Magic Border Squares
Modified Non-Normal Central Column (Type B)
1. New Shift Wheel and Transposed Shift Wheel magic 5x5 border squares (Part Q1)
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part Q2)
3. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part Q3)
4. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part Q4)
  
Section IIG
Novel New Shift Wheel and Central Column Transposed Shift Wheel Magic Border Squares
Modified Non-Normal Central Column (Type C)
1. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part R1)
2. New Shift Wheel and Transposed Shift Wheel magic 7x7 border squares (Part R2)
3. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part R3)
4. New Shift Wheel and Transposed Shift Wheel magic 9x9 border squares (Part R4)
5. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part R5)
6. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part R6)
7. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part R7)
8. New Shift Wheel and Transposed Shift Wheel magic 11x11 border squares (Part R8)
  
Section IIH
Novel New Magic Wheel Border Squares
Modified Non-Normal Central Column (Type C)
1. New Spoke Shifted Magic Wheel 7x7 border squares (Part S1)
2. New Spoke Shifted Magic Wheel 7x7 border squares (Part S2)
3. New Spoke Shifted Magic Wheel 9x9 border squares (Part S3)
4. New Spoke Shifted Magic Wheel 11x11 border squares (Part S4)
  
Section IIJ
Novel New Magic Wheel Border Squares
Modified Non-Normal Central Column (Type C)
1. New Spoke Shifted Magic Wheel 7x7 border squares (Part T1)
2. New Spoke Shifted Magic Wheel 9x9 border squares (Part T2)
3. New Spoke Shifted Magic Wheel 11x11 border squares (Part T3)
  
Section IIK
Novel New Magic Wheel Border Squares
Modified Non-Normal Central Column (Type C)
1. New Spoke Shifted Magic Wheel 7x7 border squares (Part U1)
2. New Spoke Shifted Magic Wheel 9x9 border squares (Part U2)
3. New Spoke Shifted Magic Wheel 11x11 border squares (Part U3)
  
Section IIL
Novel New Magic Wheel Border Squares
Modified Non-Normal Central Column (Type C)
1. New Spoke Shifted Magic Wheel 9x9 border squares (Part V1)
2. New Spoke Shifted Magic Wheel 11x11 border squares (Part V2)
  
Section IIM
Novel New Magic Wheel Border Squares
Modified Non-Normal Central Column (Type C)
1. New Spoke Shifted Magic Wheel 7x7 border squares (Part W1)
2. New Spoke Shifted Magic Wheel 7x7 border squares (Part W2)
3. New Spoke Shifted Magic Wheel 9x9 border squares (Part W3)
4. New Spoke Shifted Magic Wheel 9x9 border squares (Part W4)
5. New Spoke Shifted Magic Wheel 11x11 border squares (Part W5)
6. New Spoke Shifted Magic Wheel 11x11 border squares (Part W6)
  

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