"... the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch."
Leonardo's observation, verified.
२६ डिसेंबर, २०११
याची सदस्यत्व घ्या:
टिप्पणी पोस्ट करा (Atom)
skip to main |
skip to sidebar
To live freely in writing...
Encourage Althouse by doing your Amazon shopping...
... going in through the Althouse Amazon link.
Amazon
I am a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for me to earn fees by linking to Amazon.com and affiliated sites.
Encourage Althouse by making a donation:
Make a 1-time donation or set up a monthly donation of any amount you choose:
पोस्ट्स
Blog Archive
-
►
2024
(2916)
- 12/22 (19)
- 12/15 (48)
- 12/08 (64)
- 12/01 (58)
- 11/24 (57)
- 11/17 (58)
- 11/10 (52)
- 11/03 (62)
- 10/27 (62)
- 10/20 (49)
- 10/13 (49)
- 10/06 (59)
- 09/29 (58)
- 09/22 (62)
- 09/15 (52)
- 09/08 (58)
- 09/01 (56)
- 08/25 (51)
- 08/18 (57)
- 08/11 (54)
- 08/04 (64)
- 07/28 (60)
- 07/21 (75)
- 07/14 (69)
- 07/07 (63)
- 06/30 (49)
- 06/23 (68)
- 06/16 (58)
- 06/09 (61)
- 06/02 (59)
- 05/26 (56)
- 05/19 (54)
- 05/12 (53)
- 05/05 (56)
- 04/28 (65)
- 04/21 (57)
- 04/14 (68)
- 04/07 (56)
- 03/31 (55)
- 03/24 (56)
- 03/17 (59)
- 03/10 (52)
- 03/03 (63)
- 02/25 (59)
- 02/18 (45)
- 02/11 (60)
- 02/04 (56)
- 01/28 (50)
- 01/21 (64)
- 01/14 (62)
- 01/07 (59)
-
►
2023
(3115)
- 12/31 (58)
- 12/24 (43)
- 12/17 (55)
- 12/10 (66)
- 12/03 (57)
- 11/26 (56)
- 11/19 (44)
- 11/12 (55)
- 11/05 (69)
- 10/29 (63)
- 10/22 (54)
- 10/15 (62)
- 10/08 (69)
- 10/01 (70)
- 09/24 (55)
- 09/17 (49)
- 09/10 (62)
- 09/03 (54)
- 08/27 (54)
- 08/20 (45)
- 08/13 (50)
- 08/06 (54)
- 07/30 (62)
- 07/23 (50)
- 07/16 (49)
- 07/09 (59)
- 07/02 (61)
- 06/25 (63)
- 06/18 (53)
- 06/11 (63)
- 06/04 (67)
- 05/28 (53)
- 05/21 (60)
- 05/14 (66)
- 05/07 (66)
- 04/30 (67)
- 04/23 (54)
- 04/16 (55)
- 04/09 (64)
- 04/02 (63)
- 03/26 (64)
- 03/19 (76)
- 03/12 (60)
- 03/05 (52)
- 02/26 (63)
- 02/19 (49)
- 02/12 (66)
- 02/05 (63)
- 01/29 (60)
- 01/22 (57)
- 01/15 (60)
- 01/08 (66)
- 01/01 (60)
-
►
2022
(3553)
- 12/25 (55)
- 12/18 (56)
- 12/11 (73)
- 12/04 (71)
- 11/27 (76)
- 11/20 (76)
- 11/13 (80)
- 11/06 (71)
- 10/30 (72)
- 10/23 (60)
- 10/16 (61)
- 10/09 (63)
- 10/02 (70)
- 09/25 (56)
- 09/18 (62)
- 09/11 (64)
- 09/04 (76)
- 08/28 (75)
- 08/21 (63)
- 08/14 (71)
- 08/07 (76)
- 07/31 (74)
- 07/24 (71)
- 07/17 (66)
- 07/10 (67)
- 07/03 (70)
- 06/26 (73)
- 06/19 (79)
- 06/12 (74)
- 06/05 (87)
- 05/29 (54)
- 05/22 (66)
- 05/15 (72)
- 05/08 (76)
- 05/01 (62)
- 04/24 (62)
- 04/17 (70)
- 04/10 (69)
- 04/03 (82)
- 03/27 (67)
- 03/20 (64)
- 03/13 (64)
- 03/06 (79)
- 02/27 (64)
- 02/20 (66)
- 02/13 (68)
- 02/06 (59)
- 01/30 (70)
- 01/23 (58)
- 01/16 (61)
- 01/09 (64)
- 01/02 (68)
-
►
2021
(3054)
- 12/26 (55)
- 12/19 (52)
- 12/12 (53)
- 12/05 (51)
- 11/28 (44)
- 11/21 (62)
- 11/14 (54)
- 11/07 (54)
- 10/31 (65)
- 10/24 (73)
- 10/17 (61)
- 10/10 (62)
- 10/03 (64)
- 09/26 (59)
- 09/19 (48)
- 09/12 (53)
- 09/05 (60)
- 08/29 (76)
- 08/22 (67)
- 08/15 (66)
- 08/08 (53)
- 08/01 (55)
- 07/25 (56)
- 07/18 (58)
- 07/11 (59)
- 07/04 (52)
- 06/27 (57)
- 06/20 (57)
- 06/13 (65)
- 06/06 (64)
- 05/30 (50)
- 05/23 (64)
- 05/16 (56)
- 05/09 (65)
- 05/02 (63)
- 04/25 (62)
- 04/18 (56)
- 04/11 (64)
- 04/04 (71)
- 03/28 (68)
- 03/21 (57)
- 03/14 (66)
- 03/07 (60)
- 02/28 (53)
- 02/21 (56)
- 02/14 (40)
- 02/07 (62)
- 01/31 (53)
- 01/24 (61)
- 01/17 (56)
- 01/10 (58)
- 01/03 (58)
-
►
2020
(3644)
- 12/27 (49)
- 12/20 (40)
- 12/13 (56)
- 12/06 (61)
- 11/29 (57)
- 11/22 (59)
- 11/15 (57)
- 11/08 (71)
- 11/01 (76)
- 10/25 (68)
- 10/18 (69)
- 10/11 (64)
- 10/04 (70)
- 09/27 (71)
- 09/20 (64)
- 09/13 (61)
- 09/06 (70)
- 08/30 (72)
- 08/23 (78)
- 08/16 (71)
- 08/09 (50)
- 08/02 (76)
- 07/26 (62)
- 07/19 (70)
- 07/12 (64)
- 07/05 (74)
- 06/28 (84)
- 06/21 (88)
- 06/14 (73)
- 06/07 (91)
- 05/31 (99)
- 05/24 (82)
- 05/17 (76)
- 05/10 (93)
- 05/03 (78)
- 04/26 (72)
- 04/19 (63)
- 04/12 (71)
- 04/05 (74)
- 03/29 (79)
- 03/22 (64)
- 03/15 (83)
- 03/08 (75)
- 03/01 (78)
- 02/23 (70)
- 02/16 (69)
- 02/09 (67)
- 02/02 (81)
- 01/26 (68)
- 01/19 (61)
- 01/12 (63)
- 01/05 (62)
-
►
2019
(3453)
- 12/29 (81)
- 12/22 (51)
- 12/15 (74)
- 12/08 (73)
- 12/01 (66)
- 11/24 (74)
- 11/17 (77)
- 11/10 (68)
- 11/03 (69)
- 10/27 (83)
- 10/20 (83)
- 10/13 (92)
- 10/06 (65)
- 09/29 (49)
- 09/22 (60)
- 09/15 (68)
- 09/08 (67)
- 09/01 (54)
- 08/25 (64)
- 08/18 (61)
- 08/11 (56)
- 08/04 (57)
- 07/28 (53)
- 07/21 (68)
- 07/14 (61)
- 07/07 (60)
- 06/30 (65)
- 06/23 (67)
- 06/16 (54)
- 06/09 (42)
- 06/02 (64)
- 05/26 (62)
- 05/19 (60)
- 05/12 (64)
- 05/05 (77)
- 04/28 (78)
- 04/21 (43)
- 04/14 (58)
- 04/07 (67)
- 03/31 (75)
- 03/24 (65)
- 03/17 (68)
- 03/10 (70)
- 03/03 (71)
- 02/24 (62)
- 02/17 (88)
- 02/10 (72)
- 02/03 (55)
- 01/27 (68)
- 01/20 (72)
- 01/13 (76)
- 01/06 (76)
-
►
2018
(3410)
- 12/30 (59)
- 12/23 (45)
- 12/16 (76)
- 12/09 (83)
- 12/02 (69)
- 11/25 (68)
- 11/18 (61)
- 11/11 (61)
- 11/04 (68)
- 10/28 (76)
- 10/21 (71)
- 10/14 (53)
- 10/07 (53)
- 09/30 (61)
- 09/23 (61)
- 09/16 (63)
- 09/09 (57)
- 09/02 (55)
- 08/26 (54)
- 08/19 (63)
- 08/12 (59)
- 08/05 (69)
- 07/29 (64)
- 07/22 (60)
- 07/15 (69)
- 07/08 (67)
- 07/01 (67)
- 06/24 (62)
- 06/17 (68)
- 06/10 (65)
- 06/03 (65)
- 05/27 (54)
- 05/20 (63)
- 05/13 (53)
- 05/06 (78)
- 04/29 (74)
- 04/22 (68)
- 04/15 (71)
- 04/08 (53)
- 04/01 (76)
- 03/25 (64)
- 03/18 (78)
- 03/11 (67)
- 03/04 (71)
- 02/25 (66)
- 02/18 (70)
- 02/11 (64)
- 02/04 (68)
- 01/28 (80)
- 01/21 (73)
- 01/14 (65)
- 01/07 (82)
-
►
2017
(3818)
- 12/31 (85)
- 12/24 (66)
- 12/17 (75)
- 12/10 (74)
- 12/03 (77)
- 11/26 (75)
- 11/19 (58)
- 11/12 (70)
- 11/05 (75)
- 10/29 (67)
- 10/22 (76)
- 10/15 (72)
- 10/08 (70)
- 10/01 (63)
- 09/24 (59)
- 09/17 (63)
- 09/10 (65)
- 09/03 (66)
- 08/27 (69)
- 08/20 (59)
- 08/13 (66)
- 08/06 (73)
- 07/30 (89)
- 07/23 (79)
- 07/16 (81)
- 07/09 (75)
- 07/02 (64)
- 06/25 (83)
- 06/18 (70)
- 06/11 (67)
- 06/04 (74)
- 05/28 (75)
- 05/21 (77)
- 05/14 (81)
- 05/07 (89)
- 04/30 (83)
- 04/23 (80)
- 04/16 (71)
- 04/09 (78)
- 04/02 (74)
- 03/26 (83)
- 03/19 (74)
- 03/12 (77)
- 03/05 (60)
- 02/26 (49)
- 02/19 (72)
- 02/12 (74)
- 02/05 (88)
- 01/29 (91)
- 01/22 (82)
- 01/15 (47)
- 01/08 (60)
- 01/01 (48)
-
►
2016
(3557)
- 12/25 (61)
- 12/18 (62)
- 12/11 (59)
- 12/04 (60)
- 11/27 (74)
- 11/20 (68)
- 11/13 (79)
- 11/06 (62)
- 10/30 (88)
- 10/23 (75)
- 10/16 (68)
- 10/09 (58)
- 10/02 (72)
- 09/25 (70)
- 09/18 (70)
- 09/11 (79)
- 09/04 (64)
- 08/28 (53)
- 08/21 (62)
- 08/14 (70)
- 08/07 (67)
- 07/31 (68)
- 07/24 (57)
- 07/17 (71)
- 07/10 (53)
- 07/03 (53)
- 06/26 (80)
- 06/19 (81)
- 06/12 (73)
- 06/05 (65)
- 05/29 (74)
- 05/22 (67)
- 05/15 (70)
- 05/08 (89)
- 05/01 (79)
- 04/24 (67)
- 04/17 (59)
- 04/10 (61)
- 04/03 (52)
- 03/27 (68)
- 03/20 (76)
- 03/13 (68)
- 03/06 (81)
- 02/28 (65)
- 02/21 (69)
- 02/14 (70)
- 02/07 (75)
- 01/31 (68)
- 01/24 (59)
- 01/17 (69)
- 01/10 (80)
- 01/03 (69)
-
►
2015
(3788)
- 12/27 (71)
- 12/20 (68)
- 12/13 (81)
- 12/06 (70)
- 11/29 (78)
- 11/22 (58)
- 11/15 (76)
- 11/08 (84)
- 11/01 (73)
- 10/25 (74)
- 10/18 (65)
- 10/11 (75)
- 10/04 (87)
- 09/27 (59)
- 09/20 (71)
- 09/13 (55)
- 09/06 (63)
- 08/30 (72)
- 08/23 (70)
- 08/16 (70)
- 08/09 (65)
- 08/02 (65)
- 07/26 (55)
- 07/19 (66)
- 07/12 (69)
- 07/05 (62)
- 06/28 (83)
- 06/21 (79)
- 06/14 (69)
- 06/07 (81)
- 05/31 (84)
- 05/24 (78)
- 05/17 (90)
- 05/10 (85)
- 05/03 (86)
- 04/26 (77)
- 04/19 (78)
- 04/12 (63)
- 04/05 (63)
- 03/29 (79)
- 03/22 (73)
- 03/15 (63)
- 03/08 (79)
- 03/01 (66)
- 02/22 (82)
- 02/15 (78)
- 02/08 (67)
- 02/01 (84)
- 01/25 (79)
- 01/18 (63)
- 01/11 (87)
- 01/04 (70)
-
►
2014
(3825)
- 12/28 (62)
- 12/21 (44)
- 12/14 (78)
- 12/07 (97)
- 11/30 (84)
- 11/23 (82)
- 11/16 (70)
- 11/09 (71)
- 11/02 (91)
- 10/26 (79)
- 10/19 (71)
- 10/12 (86)
- 10/05 (61)
- 09/28 (58)
- 09/21 (67)
- 09/14 (56)
- 09/07 (70)
- 08/31 (64)
- 08/24 (63)
- 08/17 (51)
- 08/10 (79)
- 08/03 (71)
- 07/27 (75)
- 07/20 (81)
- 07/13 (75)
- 07/06 (67)
- 06/29 (41)
- 06/22 (80)
- 06/15 (78)
- 06/08 (91)
- 06/01 (59)
- 05/25 (58)
- 05/18 (90)
- 05/11 (73)
- 05/04 (72)
- 04/27 (72)
- 04/20 (73)
- 04/13 (82)
- 04/06 (81)
- 03/30 (77)
- 03/23 (66)
- 03/16 (56)
- 03/09 (77)
- 03/02 (90)
- 02/23 (73)
- 02/16 (91)
- 02/09 (77)
- 02/02 (91)
- 01/26 (86)
- 01/19 (81)
- 01/12 (90)
- 01/05 (67)
-
►
2013
(5117)
- 12/29 (83)
- 12/22 (82)
- 12/15 (51)
- 12/08 (95)
- 12/01 (87)
- 11/24 (79)
- 11/17 (71)
- 11/10 (94)
- 11/03 (86)
- 10/27 (73)
- 10/20 (88)
- 10/13 (79)
- 10/06 (65)
- 09/29 (65)
- 09/22 (78)
- 09/15 (81)
- 09/08 (77)
- 09/01 (79)
- 08/25 (79)
- 08/18 (96)
- 08/11 (64)
- 08/04 (82)
- 07/28 (84)
- 07/21 (110)
- 07/14 (112)
- 07/07 (91)
- 06/30 (101)
- 06/23 (101)
- 06/16 (106)
- 06/09 (133)
- 06/02 (111)
- 05/26 (86)
- 05/19 (126)
- 05/12 (125)
- 05/05 (133)
- 04/28 (103)
- 04/21 (126)
- 04/14 (98)
- 04/07 (100)
- 03/31 (110)
- 03/24 (121)
- 03/17 (120)
- 03/10 (102)
- 03/03 (98)
- 02/24 (129)
- 02/17 (104)
- 02/10 (116)
- 02/03 (135)
- 01/27 (125)
- 01/20 (125)
- 01/13 (123)
- 01/06 (129)
-
►
2012
(4971)
- 12/30 (88)
- 12/23 (103)
- 12/16 (129)
- 12/09 (120)
- 12/02 (126)
- 11/25 (98)
- 11/18 (62)
- 11/11 (87)
- 11/04 (111)
- 10/28 (98)
- 10/21 (105)
- 10/14 (101)
- 10/07 (94)
- 09/30 (90)
- 09/23 (83)
- 09/16 (93)
- 09/09 (114)
- 09/02 (93)
- 08/26 (91)
- 08/19 (103)
- 08/12 (68)
- 08/05 (74)
- 07/29 (108)
- 07/22 (117)
- 07/15 (93)
- 07/08 (88)
- 07/01 (85)
- 06/24 (76)
- 06/17 (92)
- 06/10 (126)
- 06/03 (96)
- 05/27 (100)
- 05/20 (124)
- 05/13 (99)
- 05/06 (110)
- 04/29 (87)
- 04/22 (98)
- 04/15 (82)
- 04/08 (87)
- 04/01 (90)
- 03/25 (85)
- 03/18 (98)
- 03/11 (94)
- 03/04 (96)
- 02/26 (91)
- 02/19 (88)
- 02/12 (74)
- 02/05 (78)
- 01/29 (74)
- 01/22 (80)
- 01/15 (77)
- 01/08 (71)
- 01/01 (76)
-
▼
2011
(4463)
- 12/25 (93)
- 12/18 (87)
- 12/11 (88)
- 12/04 (73)
- 11/27 (84)
- 11/20 (71)
- 11/13 (77)
- 11/06 (78)
- 10/30 (70)
- 10/23 (79)
- 10/16 (95)
- 10/09 (77)
- 10/02 (99)
- 09/25 (82)
- 09/18 (91)
- 09/11 (79)
- 09/04 (83)
- 08/28 (82)
- 08/21 (91)
- 08/14 (80)
- 08/07 (89)
- 07/31 (69)
- 07/24 (102)
- 07/17 (66)
- 07/10 (90)
- 07/03 (89)
- 06/26 (69)
- 06/19 (80)
- 06/12 (93)
- 06/05 (110)
- 05/29 (90)
- 05/22 (88)
- 05/15 (92)
- 05/08 (83)
- 05/01 (95)
- 04/24 (84)
- 04/17 (77)
- 04/10 (90)
- 04/03 (96)
- 03/27 (83)
- 03/20 (96)
- 03/13 (97)
- 03/06 (105)
- 02/27 (91)
- 02/20 (83)
- 02/13 (79)
- 02/06 (75)
- 01/30 (78)
- 01/23 (78)
- 01/16 (104)
- 01/09 (80)
- 01/02 (103)
-
►
2010
(3835)
- 12/26 (73)
- 12/19 (72)
- 12/12 (96)
- 12/05 (76)
- 11/28 (77)
- 11/21 (75)
- 11/14 (92)
- 11/07 (82)
- 10/31 (84)
- 10/24 (64)
- 10/17 (79)
- 10/10 (84)
- 10/03 (88)
- 09/26 (77)
- 09/19 (69)
- 09/12 (73)
- 09/05 (62)
- 08/29 (67)
- 08/22 (65)
- 08/15 (82)
- 08/08 (67)
- 08/01 (83)
- 07/25 (67)
- 07/18 (76)
- 07/11 (73)
- 07/04 (60)
- 06/27 (86)
- 06/20 (66)
- 06/13 (57)
- 06/06 (53)
- 05/30 (79)
- 05/23 (88)
- 05/16 (85)
- 05/09 (81)
- 05/02 (81)
- 04/25 (71)
- 04/18 (61)
- 04/11 (80)
- 04/04 (62)
- 03/28 (64)
- 03/21 (66)
- 03/14 (49)
- 03/07 (71)
- 02/28 (76)
- 02/21 (66)
- 02/14 (82)
- 02/07 (61)
- 01/31 (79)
- 01/24 (87)
- 01/17 (80)
- 01/10 (72)
- 01/03 (69)
-
►
2009
(3716)
- 12/27 (58)
- 12/20 (53)
- 12/13 (84)
- 12/06 (77)
- 11/29 (78)
- 11/22 (50)
- 11/15 (83)
- 11/08 (78)
- 11/01 (74)
- 10/25 (85)
- 10/18 (69)
- 10/11 (63)
- 10/04 (91)
- 09/27 (86)
- 09/20 (82)
- 09/13 (60)
- 09/06 (64)
- 08/30 (81)
- 08/23 (82)
- 08/16 (72)
- 08/09 (70)
- 08/02 (45)
- 07/26 (76)
- 07/19 (71)
- 07/12 (42)
- 07/05 (57)
- 06/28 (105)
- 06/21 (86)
- 06/14 (71)
- 06/07 (83)
- 05/31 (83)
- 05/24 (57)
- 05/17 (74)
- 05/10 (83)
- 05/03 (57)
- 04/26 (70)
- 04/19 (67)
- 04/12 (82)
- 04/05 (63)
- 03/29 (62)
- 03/22 (67)
- 03/15 (68)
- 03/08 (50)
- 03/01 (60)
- 02/22 (53)
- 02/15 (55)
- 02/08 (68)
- 02/01 (89)
- 01/25 (81)
- 01/18 (83)
- 01/11 (91)
- 01/04 (77)
-
►
2008
(3407)
- 12/28 (75)
- 12/21 (44)
- 12/14 (63)
- 12/07 (78)
- 11/30 (87)
- 11/23 (68)
- 11/16 (75)
- 11/09 (85)
- 11/02 (81)
- 10/26 (79)
- 10/19 (86)
- 10/12 (70)
- 10/05 (66)
- 09/28 (76)
- 09/21 (84)
- 09/14 (75)
- 09/07 (73)
- 08/31 (81)
- 08/24 (75)
- 08/17 (73)
- 08/10 (73)
- 08/03 (56)
- 07/27 (57)
- 07/20 (55)
- 07/13 (42)
- 07/06 (47)
- 06/29 (58)
- 06/22 (62)
- 06/15 (53)
- 06/08 (65)
- 06/01 (53)
- 05/25 (45)
- 05/18 (62)
- 05/11 (73)
- 05/04 (69)
- 04/27 (69)
- 04/20 (68)
- 04/13 (64)
- 04/06 (63)
- 03/30 (49)
- 03/23 (54)
- 03/16 (56)
- 03/09 (72)
- 03/02 (70)
- 02/24 (61)
- 02/17 (62)
- 02/10 (68)
- 02/03 (60)
- 01/27 (58)
- 01/20 (51)
- 01/13 (49)
- 01/06 (69)
-
►
2007
(2915)
- 12/30 (67)
- 12/23 (50)
- 12/16 (51)
- 12/09 (51)
- 12/02 (50)
- 11/25 (51)
- 11/18 (57)
- 11/11 (64)
- 11/04 (68)
- 10/28 (57)
- 10/21 (55)
- 10/14 (57)
- 10/07 (52)
- 09/30 (60)
- 09/23 (66)
- 09/16 (39)
- 09/09 (61)
- 09/02 (65)
- 08/26 (54)
- 08/19 (55)
- 08/12 (58)
- 08/05 (59)
- 07/29 (53)
- 07/22 (58)
- 07/15 (51)
- 07/08 (63)
- 07/01 (66)
- 06/24 (54)
- 06/17 (45)
- 06/10 (55)
- 06/03 (69)
- 05/27 (60)
- 05/20 (68)
- 05/13 (72)
- 05/06 (56)
- 04/29 (49)
- 04/22 (52)
- 04/15 (52)
- 04/08 (50)
- 04/01 (41)
- 03/25 (50)
- 03/18 (50)
- 03/11 (62)
- 03/04 (54)
- 02/25 (47)
- 02/18 (53)
- 02/11 (50)
- 02/04 (61)
- 01/28 (65)
- 01/21 (50)
- 01/14 (51)
- 01/07 (61)
-
►
2006
(2745)
- 12/31 (53)
- 12/24 (55)
- 12/17 (54)
- 12/10 (65)
- 12/03 (82)
- 11/26 (50)
- 11/19 (54)
- 11/12 (58)
- 11/05 (65)
- 10/29 (56)
- 10/22 (64)
- 10/15 (63)
- 10/08 (55)
- 10/01 (60)
- 09/24 (59)
- 09/17 (43)
- 09/10 (36)
- 09/03 (56)
- 08/27 (54)
- 08/20 (47)
- 08/13 (54)
- 08/06 (51)
- 07/30 (47)
- 07/23 (45)
- 07/16 (42)
- 07/09 (60)
- 07/02 (46)
- 06/25 (52)
- 06/18 (50)
- 06/11 (55)
- 06/04 (54)
- 05/28 (41)
- 05/21 (54)
- 05/14 (47)
- 05/07 (63)
- 04/30 (52)
- 04/23 (40)
- 04/16 (38)
- 04/09 (54)
- 04/02 (48)
- 03/26 (52)
- 03/19 (45)
- 03/12 (47)
- 03/05 (49)
- 02/26 (46)
- 02/19 (50)
- 02/12 (43)
- 02/05 (47)
- 01/29 (56)
- 01/22 (45)
- 01/15 (44)
- 01/08 (44)
- 01/01 (55)
-
►
2005
(2920)
- 12/25 (56)
- 12/18 (49)
- 12/11 (67)
- 12/04 (73)
- 11/27 (62)
- 11/20 (65)
- 11/13 (67)
- 11/06 (68)
- 10/30 (64)
- 10/23 (64)
- 10/16 (68)
- 10/09 (61)
- 10/02 (75)
- 09/25 (59)
- 09/18 (58)
- 09/11 (54)
- 09/04 (57)
- 08/28 (82)
- 08/21 (58)
- 08/14 (67)
- 08/07 (61)
- 07/31 (54)
- 07/24 (62)
- 07/17 (70)
- 07/10 (59)
- 07/03 (65)
- 06/26 (78)
- 06/19 (53)
- 06/12 (54)
- 06/05 (44)
- 05/29 (51)
- 05/22 (53)
- 05/15 (34)
- 05/08 (38)
- 05/01 (61)
- 04/24 (55)
- 04/17 (55)
- 04/10 (63)
- 04/03 (61)
- 03/27 (51)
- 03/20 (42)
- 03/13 (57)
- 03/06 (45)
- 02/27 (48)
- 02/20 (44)
- 02/13 (36)
- 02/06 (50)
- 01/30 (50)
- 01/23 (37)
- 01/16 (29)
- 01/09 (41)
- 01/02 (45)
-
►
2004
(2035)
- 12/26 (48)
- 12/19 (41)
- 12/12 (46)
- 12/05 (47)
- 11/28 (53)
- 11/21 (45)
- 11/14 (46)
- 11/07 (60)
- 10/31 (48)
- 10/24 (45)
- 10/17 (60)
- 10/10 (37)
- 10/03 (42)
- 09/26 (37)
- 09/19 (46)
- 09/12 (30)
- 09/05 (40)
- 08/29 (43)
- 08/22 (39)
- 08/15 (27)
- 08/08 (36)
- 08/01 (32)
- 07/25 (43)
- 07/18 (28)
- 07/11 (35)
- 07/04 (34)
- 06/27 (31)
- 06/20 (35)
- 06/13 (35)
- 06/06 (21)
- 05/30 (32)
- 05/23 (40)
- 05/16 (35)
- 05/09 (46)
- 05/02 (52)
- 04/25 (52)
- 04/18 (45)
- 04/11 (36)
- 04/04 (37)
- 03/28 (31)
- 03/21 (40)
- 03/14 (33)
- 03/07 (36)
- 02/29 (41)
- 02/22 (31)
- 02/15 (33)
- 02/08 (43)
- 02/01 (33)
- 01/25 (43)
- 01/18 (56)
- 01/11 (30)
२३ टिप्पण्या:
Ol' Leo was the first thinker I really got into as a child. I think Abraham Lincoln came next.
The man was just brilliant,...so unlike what we get today,...
I think I shall never see a poem as lovely as a tree; poems are made by fools like me, but Only God can make a tree.
Wisdom does great work.
It must mean the cross section area.
The sap flow below the branching equals the sap flow above.
The flow is proportional to the area.
It's not wind planning.
Intelligent Design or Evolution?
This Leonardo dude never studied any giant Redwoods.
rhhardin: Thanks. The way the article (and the scientist) stated the principle made no sense whatsoever. Your clarification is likely correct.
"Intelligent Design or Evolution?"
Plant physiology.
I was one of the first people to create "fractal trees" (about 30 years ago) with computers, and made use of this pretty obvious fact, but without the stilted language.
With A Hat Tip To Roger
A mother branch and A daughter branch,
A daughter branch and a mother branch,
Some can and some can and some can't.
It's my belief that pride is the chief tranche
In the number of daughters that decline
To branch off the mother branch.
What happen when it's tow son branches?
I had a discrete math teacher who mentioned that the secret to mathematics was patterns and the great minds always sought them out.
Leo was no different.
Tow tow tow your boat....
"When a mother branch branches in two daughter branches, the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch."
Translation: The surface areas of the two daughter branches add up to the surface area of the mother branch.
Does NPR think its audience can't figure out what was meant by the first version?
The premise of the paper is: Examining botanical trees, Leonardo da Vinci noted that the total cross section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads.
Sap flow has a lot of variables, what would this do that would influence it enough to matter?
I also think rhhardin is saying the simplest answer. The tree is mostly made of a lot of thin tubes running together along the branch. The cross-sectional area is more-or-less the sum of the cross-sectional area of all those little tubes. Some of the tubes go into one branch, some into the other. Net area is the same.
And probably trees handle hurricanes the same way our buildings do: There aren't that many hurricanes in a given place. Trees are built strong and have roots. A few trees fall down. More grow up before the next hurricane.
This is one of those facts that would only be surprising if it wasn't true.
If you were a tree wouldn't you do it that way, and what kind of tree would you be?
Ahh.
Wood under the microscope
"Leonardo's observation, verified."
We think we're so smart, yet it is edifying to be reminded occasionally we stand on the shoulders of the giants who preceded us.
Now for my own observation:
Blanches "have always depended on the kindness of strangers."
Duh.
Ann, this guy is ripping off Adrian Bejan's work on the constructal law, which likewise appeals to Leonardo. Bejan published a paper on this issue with Sylvie Lorente in 2008. NPR should know better.
Bejan's trade book, 'Design in Nature', is coming out in January. Don't worry, I'm planning on buying it through the amazon links on your blog.
http://www.amazon.com/Design-Nature-Constructal-Technology-Organization/dp/0385534612/ref=sr_1_1?ie=UTF8&qid=1324925625&sr=8-1
With A Hat Tip To Roger II
Dang me, dang me,
Oughta take a rope an' hang me,
Hang me from the highest daughter branch,
Mother branch would you weep for me?
टिप्पणी पोस्ट करा