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Topic: Updated EMLR and 2/n table links ... narratives are available
Replies: 8   Last Post: Apr 6, 2011 7:50 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Updated EMLR and 2/n table links ... narratives are available
Posted: Mar 23, 2011 8:29 AM

1. (1/8)(5/5) = 5/40 = (4 + 1)/40 = 1/10 + 1/40

2. (1/4)(5/5)= 5/20 = (4 +1)/20= 1/5 + 1/20

3. (1/3)(3/3)) = 3/9 = (2 + 1)/9 = 1/4 + 1/12

4. (1/5)(2/2)) = 2/10 = 1/10 + 1/10

5. (1/3)(2/2) = 2/6= 1/6 + 1/6

6. (1/2)(3/3) = 3/6= 1/6 + 1/6 + 1/6

7. 2/3 = 1/3 + 1/3

8. (1/8)(25/25)= 25/200 = (8 +17)/200 =
1/25 + (17/200)(6/6) = 1/25 + (80 + 16 + 6)/1200 =
1/8 = 1/25 + 1/15 + 1/75 + 1/200

9. (1/16)(25/25)= 25/400 = (8 +17)/400 =
1/50 + (17/2400)(6/6) = 1/50 + (80 + 16 + 6)/2400 =
1/16 = 1/50 + 1/30 + 1/150 + 1/400

10. (1/15)(10/10) = 10/150 = ( 6 + 3 + 1)/150 =
1/25 + 1/50 + 1/150, (1/6 was initial term)

11. ( 1/6)(3/3) = 3/18 = (2 + 1)/18 = 1/9 + 1/18
12. (1/4)(7/7) = 7/28 = (4 + 2 + 1)/28 =
1/7 + 1/14 + 1/28

13. (1/8)(3/3) = 3/24 = (2 + 1)/24 = 1/12 + 1/24
14. ( 1/7)(6/6) = 6/42 = (3 + 2 + 1)/42=
1/14 + 1/21 + 1/42

15. (1/9)(6/6) = 6/54 = (3 + 2 + 1)/54 =
1/18 + 1/27 + 1/54

16. (1/11)(6/6) = 6/66 = (3 + 2 + 1)/66=
1/22 + 1/33 + 1/66

17. (1/13)(?) = 1/28 + 1/49 + 1/196 (corrected by?)
(1/13)(6/6) = 6/78 = (3 + 2 + 1)/78 =1/26 + 1/39 + 1/78

18. (1/15)(6/6) = 6/90 = (3 + 2+ 1)/90 =
1/30 + 1/45 + 1/90

19. (1/16)(3/3) = 3/48 = (2 + 1)/48 = 1/24 + 1/48

20. (1/12)(3/3) = 3/36 = ( 2 + 1)/36 = 1/18 + 1/36

21. (1/14)(3/3) = 3/42 = (2 + 1)/42 = 1/21 + 1/42

22. (1/30)(3/3)= 3/90 = (2 + 1)/90 = 1/45 + 1/90

23. (1/20)(3/3)= 3/60 = (2 + 1)/60 = 1/30 + 1/60

24. (1/10)(3/3) = 3/30 = (2 + 1)/30 = 1/15 + 1/30

25. (1/32)(3/3)= 3/96 = (2 + 1)/96= 1/48 + 1/96

26. (1/64)(3/3) = 3/192 = (2 + 1)/192 = 1/96 + 1/192

Further discussed by:
http://planetmath.org/encyclopedia/EgyptianMathematicalLeatherRoll2.html
http://en.wikipedia.org/wiki/Egyptian_Mathematical_Leather_Roll
http://mathworld.wolfram.com/EgyptianMathematicalLeatherRoll.html

Note the links to the 2/n table's LCMs and red auxiliaries

http://rmprectotable.blogspot.com/

1. 2/3 = 1/3 + 1/3

2. 2/5(3/3) = 6/15= (5+ 1)/15 = 1/3 + 1/15

3. 2/7(4/4) = 8/28= (7 + 1)/28 = 1/4 + 1/28

4. 2/9 (2/2) = 4/18= (3 + 1)/18 = 1/6 + 1/18

5. 2/11(6/6) = 12/66= (11 + 1)/66 = 1/6 + 1/66

6. 2/13(8/8) = 16/104= (13 + 2 + 1)/104 =
1/8 + 1/52 + 1/104

7. /15(2/2) = 4/30= (3 + 1)/30 = 1/10 + 1/30

8. 2/17(12/12) = 24/204= (17 + 4 + 3)/204 =

9. 1/12 + 1/51 + 1/68

10. 2/19(12/12) = 24/228= (19 + 3 + 2)/228 =
1/12 + 1/76 + 1/114

11. 2/21((2/2) = 4/42= (3 + 1)/42 = 1/14 + 1/42

12. 2/23(12/12) = 24/276= (23 +1)/276 = 1/12 1/276

13. 2/25(3/3) = 6/75= (5 + 1)/75 = 1/15 + 1/75

14. 2/27(2/2) = 4/54= (3 + 1)/54 = 1/18 + 1/54

15. 2/29(24/24)= 48/696= (29 + 12 + 4 + 3)/696 =
1/24 + 1/58 + 1/174 + 1/232

16. 2/31(20/20) = 40/1620= (31 + 5 + 4)/1620 =
1/20 + 1/124 + 1/155

17. 2/33(2/2) = 4/66 (3 + 1)/66 = 1/22 + 1/66

18. 2/35(30/30) = 60/1050= (35 + 25)/1050 = 1/30 + 1/42

19. 2/37(24/24) = 48/888= ( 37 + 8 + 3 )/888 =
1/24 + 1/111 + 1/296

20. 2/39(2/2)= 4/78= (3 + 1)/78 = 1/26 + 1/78

21. 2/41(24/24)= 48/984= (41 + 4 + 3 )/984 =
1/24 + 1/246 + 1/328

22. 2/43(42/42)= 84/1806= (43 + 21 + 14 + 6)/1806 =
1/42 + 1/86 + 1/129 + 1/301

23. 2/45(2/2)= 4/90= ( 3 + 1)/90 = 1/30 + 1/90

24. 2/47(30/30)= 60/1410= (47 + 10 + 3)/1410 =
1/30 + 1/141 + 1/470

25. 2/49(4/4)= 8/196= (7 + 1)/196 = 1/28 + 1/196

26. 2/51(2/2) = 4/102= (3 + 1)/102 = 1/34 + 1/102

27. 2/53(30/30)= 60/1590= (53 + 5 + 2 )/1590 =
1/30 + 1/318 + 1/795

28. 2/55(6/6) = 12/330= (11 + 1)/330 = 1/30 + 1/330

29. 2/57(2/2) = 4/114= (3 + 1)/114 = 1/38 + 1/114

30. 2/59(36/36) = 72/2124= (59 + 9 + 4) /2124 =
1/36 + 1/236 + 1/531

31. 2/61(40/40) = 80/2440= (61 + 10 + 5 + 4)/2440 =
1/40 + 244 + 1/488 + 1/610

32. 2/63(2/2)= 4/126= (3 + 1)/126 = 1/42 + 1/126

33. 2/65(3/3)= 6/195= (5 + 1)/195 = 1/39 + 1/195

34. 2/67(40/40)= 80/2680= (67 + 8 +5 )/2680 =
1/40 + 1/335 + 1/536

35. 2/69(2/2)= 4/138= (3 + 1)/138 = 1/46 +1/138

36. 2/71(40/40)= 80/2840= (71+ 5 + 4)2840 =
1/40 + 1/568 + 1/710

37. 2/73(60/60)= 120/4380= (73 + 20 + 15 + 12)/4380 =
1/60 + 1/219 + 1/292 + 1/365

38. 2/75(2/2)= 4/150= (3 +1)/150 = 1/50 + 1/150

39. 2/77(4/4)= 8/388= (7 + 1)/388 = 1/44 + 1/308

40. 2/79(60/60)= 120/4740 =(79 + 20 + 15 + 6 )/4740 =
1/60 + 237 + 1/316 + 1/790

41. 2/81(2/2)= 4/162 = (3 + 1)/162 = 1/54 + 1/162

42. 2/83(60/60)= 120/4980= (83+ 15 + 12 +10)/4980 =
1/60 + 1/332 + 1/415 + 1/498

43. 2/85(3/3)= 6/255= (5 + 1)/255 = 1/51 + 1/255

44. 2/87(2/2)= 4/174= (3 + 1)/174 = 1/58 + 1/74

45. 2/89 =(60/60)= 120/5340= (89 + 15 +10 + 6)/5340 =
1/60 + 1/356 + 1/534 + 1/890

46. 2/91(70/70) = 140/6370= (91 + 49)/6370 = 1/70 + 1/130

47. 2/93(2/2)= 4/186= (3 + 1)/186 = 1/62 + 1/186

48. 2/95(60/60) = 120/5700 = (95 + 15 + 10)/5700 =
1/60 + 1/380 + 1/570

49. 2/97(56/56)= 112/5432= (97+ 8 + 7 )/5432 =
1/56 + 1/679 + 1/776

50. 2/99 (2/2) = 4/198= (3 + 1)/198 = 1/66 + 1/198

51. 2/101(6/6)= 12/606= (6 + 3 + 2 + 1)/606 =
1/101 + 1/202 + 1/303 + 1/606

Date Subject Author
3/23/11 Milo Gardner
3/23/11 Milo Gardner
3/26/11 Milo Gardner
3/30/11 Milo Gardner
4/2/11 Milo Gardner
4/2/11 Milo Gardner
4/3/11 Milo Gardner
4/6/11 Milo Gardner
4/6/11 Milo Gardner