sacred mathematics
DESCRIPTION
Sacred Mathematics. Part 1: F.3 Sci and Math Competition. Some Variations. Solution for 2. Solution for 5. Solution for 3. 商高定理. Euclid II.14. F.3 Textbook Irrational No. 36. a. 9. b. r. Part 2: F.4 Circles & Tangents. 36. b. 9. 36. 2. c. 9. 1. b = 36 – 9 = 27 - PowerPoint PPT PresentationTRANSCRIPT
Sacred Mathematics
Part 1: F.3 Sci and Math Competition
Some Variations
Solution for 2
Solution for 5
Solution for 3
商高定理
青 出
青 入
青出
青入
朱出
朱入
青 朱
Euclid II.14
F.3 Textbook Irrational No.
36
9a
b
r
Part 2: F.4 Circles & Tangents
21
111
RRr
212 RRb
36
9b
c
b = 36 – 9 = 27
c = (452 – 272) = 36
369
1 2
2 21 (36 ) (36 ) 12r r r
2 22 (9 ) (9 ) 6r r r
12 6 36
4
r r
r
Sangaku Problem
9
4
)21(214
1
4
1
)2
1()
2
1(
21)1(
22
222
22
r
rrrrr
xrr
rrrx
1
r
x
Descartes Circle Theorem
1830 Hasimoto Masataka 橋本正孝 / 1643 Descartes's original drawing
Preliminary Result
))(( 3121
2212
rrrr
rAB
Preliminary Result
kr3r2
r1r1θ
21
221
21
3121
2231
221
223
22
2))((2
)()(cos
)(
r
ABrr
rrrr
krrrr
rrk
))(( 3121
2212
rrrr
rAB
Japanese Version of DCT (1)
))((
4
))((
4
))((
4
))((
)2(
332
22
32
331
12
32
3231
212
3
3231
221
232
rtrr
trrBC
rtrr
trrAC
rrrr
rrr
rrrr
rrrAB
Japanese Version of DCT (2)
))(()(
4
4
2
3322
31
232
21
23
222
3
rtrrrr
trrr
r
ACABAH
AB
AH
r
AC
CCAABH
Japanese Version of DCT (3)
))((1
))((
4
3221
21
331
12
3
222
rrrr
rr
rtrr
trr
AHACCH
CHBCBCAC
ACBCABCBCACAB
2
cos222
222
Japanese Version of DCT (4)
133221321
321321323121
321
321321323121
321
1112
1111
)(2
)(2
rrrrrrrrrt
rrrrrrrrrrrr
rrrT
rrrrrrrrrrrr
rrrt