Euler, E101, Errors

Problem and Solution

Mission, Music, Mathematics

Japanese

Leonhard Euler (1707-1783)

[Leonhard Euler]


Lyrics

Musics

Graphics

EP: 7 EP: 37 EP: 73
UBASIC Program: E101-0.UB E101-1.UB E101-2.UB E101-3.UB
E101-A.UB E101-B.UB E101-C.UB E102.UB

Exponentialibus ac Logarithmis

E101 p.75 p.76

Chap.VI
Exponentialibus ac Logarithmis

Z=5.000000
lZ = 0.698970

(2005, Nov. 28)

First error

E101 p.77

0.3010300...=log(2)/log(10)

0.3010299(correct value)
+0.0000001

1/0.3010300...=log(10)/log(2)

3.3219280(correct value)
3.3219277(p.77 in E101)
-0.0000003

The following problems

(2006, Nov., 2007 Aug.)

Great errors

E101 p.90 p.91

e

2.71828182845904523536028 (the last number is correct)
2.71828182845904523536028747135266249775724709
Round down



log n

Chap.VII
l7 +0.0000000000000000000001112
l8 +0.0000000000000000000000001
l9 +0.0000000000000000000000001

Psalm 111:2
Hll. Hll.
The works of the Lord are great,
sought out of all them that have delight therein.

777=3*7*37

Psalm 112
psalm 37=a pair of alphabetic psalms 111 & 112

the number of errors=trinity

(2005, Jul. 25)

Harmonic errors

E101 p.99 p.100 p.101

sin(m/n pi/2)

01 -0.0000000000000000000000000000
03 +0.0000000000000000000000000002
05 -0.0000000000000000000000000006
07 +0.0000000000000000000000000007
09 -0.0000000000000000000000000003
11 +0.0000000000000000000000000005
13 -0.0000000000000000000000000006
15 +0.0000000000000000000000000008
17 -0.0000000000000000000000000006
19 +0.0000000000000000000000000004
21 -0.0000000000000000000000000004
23 +0.0000000000000000000000000002
25 -0.0000000000000000000000000001
27 +0.0000000000000000000000000000
29 -0.0000000000000000000000000001


cos(m/n pi/2)

00 -0.0000000000000000000000000000
02 +0.0000000000000000000000000004
04 -0.0000000000000000000000000004
06 +0.0000000000000000000000000008
08 -0.0000000000000000000000000004
10 +0.0000000000000000000000000004
12 -0.0000000000000000000000000005
14 +0.0000000000000000000000000002
16 -0.0000000000000000000000000006
18 +0.0000000000000000000000000003
20 -0.0000000000000000000000000005
22 +0.0000000000000000000000000003
24 -0.0000000000000000000000000003
26 -0.0000000000000000000000000001
28 -0.0000000000000000000000000002
30 +0.0000000000000000000000000002

a note: 0 0 4 2 4 6 8 7 4 3 4 5 5 6 2 8 6 6 3 4 5 4 3 2 3 1 -1 0 2 1 2
euler.mid
[Euler.mid]
eulerz.mid Eulerian tuning the final score
the number of errors=28 digits=28 notes+alpha
the sum of absolute values of errors*10^28=111=3*37
the sum of errors*10^28=-3
the number of beats=59
(2005, Nov. 11-2007, May 7, August 25)

Impossible errors

E101 p.102

tan(m/n pi/2)

05 -0.0000000000001
07 -0.0000000000001
09 -0.0000000000128
11 +0.0000000000001
13 -0.0000000000001

cot(m/n pi/2)

05 -0.0000000000001
11 -0.0000000000001

The graph of the Seven Bridges of Konigsberg and its dual graph
(E53 p.128=2^7, 7=6+1=3+1+3)

---
+
---


*E*E*
EEEE
*E*

V=5 (the number of left errors)
E=7 (128=2^7)
F=4 (the number of left 1s)

V-E+F=2 (the number of right errors)

05=Co 11=Figura

the number of errors=7 bridges
the number of - or 1=6 bridges
variant and invariant

(2005, Nov. 16-2007, May 10, August 25)
Compare lists and calculations in E128
(2008, April 8)
Reg: 2005, Nov. 17
Title: Euler, E101, Errors
Method: webpage
Content:
https://math0.pm.tokushima-u.ac.jp/~hiroki/major/euler2-e.html
EP: 7
[EulerWS2012]

Index