43 planars logflat badness ordered

Here they are again in logflat badness order. The last line gives
Tenney distance , TOP error, and logflat badness.

4375/4374
[[1, 0, 0, 1], [0, 1, 0, 7], [0, 0, 1, -4]]
[1200.016360, 1901.980932, 2786.275726]
24.189805 .016361 4.668292

2401/2400
[[1, 1, 1, 2], [0, 2, 1, 1], [0, 0, 2, 1]]
[1200.032113, 350.9868928, 617.6846359]
22.458238 .032113 6.807744

225/224
[[1, 0, 0, -5], [0, 1, 0, 2], [0, 0, 1, 2]]
[1200.493660, 1901.172569, 2785.167472]
15.621136 .493660 24.496112

126/125
[[1, 0, 0, -1], [0, 1, 0, -2], [0, 0, 1, 3]]
[1199.010636, 1900.386896, 2788.610946]
13.943064 .989364 31.160753

81/80
[[1, 0, -4, 0], [0, 1, 4, 0], [0, 0, 0, 1]]
[1201.698520, 1899.262910, 3368.825906]
12.661778 1.698521 36.380484

64/63
[[1, 0, 0, 6], [0, 1, 0, -2], [0, 0, 1, 0]]
[1197.723683, 1905.562879, 2786.313714]
11.977280 2.276318 39.037716

50/49
[[2, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 1]]
[598.4467109, 1901.955001, 2779.100463]
11.258566 3.106578 41.594258

49/48
[[1, 0, 0, 2], [0, 2, 0, 1], [0, 0, 1, 0]]
[1203.187309, 953.5033827, 2786.313714]
11.199672 3.187309 41.789211

32805/32768
[[1, 0, 15, 0], [0, 1, -8, 0], [0, 0, 0, 1]]
[1200.065120, 1901.851787, 3368.825906]
30.001628 .065120 43.965846

36/35
[[1, 0, 0, 2], [0, 1, 0, 2], [0, 0, 1, -1]]
[1195.264647, 1894.449645, 2797.308862]
10.299208 4.735353 44.400354

28/27
[[1, 0, 0, -2], [0, 1, 0, 3], [0, 0, 1, 0]]
[1193.415676, 1912.390908, 2786.313714]
9.562242 6.584324 45.874248

245/243
[[1, 0, 0, 0], [0, 1, 1, 2], [0, 0, 2, -1]]
[1200., 1903.372995, 440.4316973]
15.861450 .894655 47.189574

1029/1024
[[1, 1, 0, 3], [0, 3, 0, -1], [0, 0, 1, 0]]
[1200.421488, 233.6218235, 2786.313714]
20.007027 .421488 56.277426

3136/3125
[[1, 0, 0, -3], [0, 1, 0, 0], [0, 0, 2, 5]]
[1199.738066, 1901.955001, 1393.460953]
23.224350 .261934 63.501663

6144/6125
[[1, 0, 1, 4], [0, 1, 1, -1], [0, 0, -2, 3]]
[1199.786928, 1901.617290, 157.2978838]
25.165457 .213072 71.213871

5120/5103
[[1, 0, 0, 10], [0, 1, 0, -6], [0, 0, 1, 1]]
[1199.766314, 1902.325384, 2785.771112]
24.639058 .233686 71.770898

128/125
[[3, 0, 7, 0], [0, 1, 0, 0], [0, 0, 0, 1]]
[399.0200131, 1901.955001, 3368.825906]
13.965784 2.939961 93.201243

10976/10935
[[1, 0, 2, -1], [0, 1, 2, 3], [0, 0, -3, -1]]
[1199.758595, 1902.337618, 1139.106063]
26.838730 .241405 104.378975

1728/1715
[[1, 0, 0, 2], [0, 1, 0, 1], [0, 0, 3, -1]]
[1199.391895, 1900.991178, 929.2418964]
21.498880 .608105 108.258175

16875/16807
[[1, 0, 0, 0], [0, 1, 3, 3], [0, 0, -5, -4]]
[1200., 1901.560426, 583.7891213]
28.079374 .248949 128.967040

875/864
[[1, 0, 0, 5], [0, 1, 0, 3], [0, 0, 1, -3]]
[1201.121570, 1903.732647, 2783.709509]
19.528027 1.121570 135.918456

19683/19600
[[1, 0, 0, -2], [0, 2, 0, 9], [0, 0, 1, -1]]
[1200.256485, 950.7742412, 2786.909253]
28.523229 .256485 141.473578

15625/15552
[[1, 0, 1, 0], [0, 6, 5, 0], [0, 0, 0, 1]]
[1200.291038, 317.0693810, 3368.825906]
27.856381 .291038 146.038672

4000/3969
[[1, 0, 1, 4], [0, 1, 0, -2], [0, 0, 2, 3]]
[1199.436909, 1902.847479, 792.7846742]
23.920344 .563091 153.626817

686/675
[[1, 0, 2, 1], [0, 1, 0, 1], [0, 0, 3, 2]]
[1198.513067, 1904.311735, 130.9133777]
18.820808 1.486934 155.476025

250/243
[[1, 2, 3, 0], [0, -3, -5, 0], [0, 0, 0, 1]]
[1196.905960, 162.3176609, 3368.825906]
15.890597 3.094040 164.401387

2048/2025
[[2, 0, 11, 0], [0, 1, -2, 0], [0, 0, 0, 1]]
[599.5552941, 1903.364685, 3368.825906]
21.983706 .889412 173.111327

2430/2401
[[1, 0, 3, 1], [0, 1, 3, 2], [0, 0, -4, -1]]
[1199.075238, 1900.489288, 1628.631774]
22.476160 .924762 196.669589

525/512
[[1, 0, 0, 9], [0, 1, 0, -1], [0, 0, 1, -2]]
[1202.406737, 1898.140412, 2780.725442]
18.036174 2.406738 212.238977

3125/3087
[[1, 0, 0, 0], [0, 1, 1, 1], [0, 0, 3, 5]]
[1200., 1903.401919, 293.5973664]
23.201630 .912903 220.453810

405/392
[[1, 0, 1, -1], [0, 1, 0, 2], [0, 0, 2, 1]]
[1203.269293, 1896.773294, 787.7266785]
17.276488 3.269293 242.713818

256/245
[[1, 0, 0, 4], [0, 1, 0, 0], [0, 0, 2, -1]]
[1195.228951, 1901.955001, 1398.695873]
15.936638 4.771049 256.459893

3125/3072
[[1, 0, 2, 0], [0, 5, 1, 0], [0, 0, 0, 1]]
[1201.276744, 380.7957184, 3368.825906]
23.194603 1.276744 307.943011

3645/3584
[[1, 0, 0, -9], [0, 1, 0, 6], [0, 0, 1, 1]]
[1201.235997, 1899.995991, 2783.443817]
23.639058 1.235998 321.630472

1029/1000
[[1, 0, 0, 1], [0, 3, 0, -1], [0, 0, 1, 1]]
[1202.477948, 632.6758490, 2792.067330]
19.972812 2.477948 328.600180

648/625
[[4, 0, 3, 0], [0, 1, 1, 0], [0, 0, 0, 1]]
[299.1603149, 1896.631523, 3368.825906]
18.627562 3.358741 336.991833

2240/2187
[[1, 0, 0, -6], [0, 1, 0, 7], [0, 0, 1, -1]]
[1198.134693, 1904.911442, 2781.982606]
22.224021 1.865307 379.192372

729/700
[[1, 0, 0, -2], [0, 1, 0, 6], [0, 0, 1, -2]]
[1203.706383, 1896.080523, 2794.919668]
18.960986 3.706383 399.220421

1323/1280
[[1, 0, 0, 4], [0, 1, 1, -1], [0, 0, 2, 1]]
[1202.764567, 1897.573266, 447.5797863]
20.691525 2.764567 422.294972

5103/5000
[[1, 0, 0, 3], [0, 1, 0, -6], [0, 0, 1, 4]]
[1201.434720, 1899.681024, 2789.645030]
24.604842 1.434720 438.195840

8748/8575
[[1, 0, 1, 0], [0, 1, 2, 1], [0, 0, -3, 2]]
[1198.678173, 1899.859955, 736.3383942]
26.160658 1.321827 515.926826

5625/5488
[[1, 0, 1, 0], [0, 1, 1, 2], [0, 0, -3, -4]]
[1201.715742, 1899.235615, 106.2071570]
24.879702 1.715742 547.837029

3125/3024
[[1, 0, 0, -4], [0, 1, 0, -3], [0, 0, 1, 5]]
[1202.454598, 1905.845447, 2780.614314]
23.171883 2.454598 589.718096

hey guys,

i've finally decided to enroll in school again
to study the math that i'm sorely lacking.

i know that ultimately i want to take a course
in linear algebra, and that Grassmann algebra in
particular is something i want to be familiar with.

the college catalog lists trigonometry and calculus
as prerequisites for linear algebra, so this is going
to be a long haul if i can stick with it. i nearly
bombed out of algebra II in high school, and never
studied math again after that ... except the bits
and pieces i picked up as a tuning theorist.

i feel like i'm missing out on too much new discovery
here on tuning-math, and want to get up to speed.

i haven't selected any particular classes yet.
i will certainly have to start with regular algebra
all over again, and will probably only be able to take
one course per semester. advice is appreciated.

-monz

>i've finally decided to enroll in school again
>to study the math that i'm sorely lacking.
>
>i know that ultimately i want to take a course
>in linear algebra, and that Grassmann algebra in
>particular is something i want to be familiar with.
>
>the college catalog lists trigonometry and calculus
>as prerequisites for linear algebra, so this is going
>to be a long haul if i can stick with it. i nearly
>bombed out of algebra II in high school, and never
>studied math again after that ... except the bits
>and pieces i picked up as a tuning theorist.
>
>i feel like i'm missing out on too much new discovery
>here on tuning-math, and want to get up to speed.
>
>i haven't selected any particular classes yet.
>i will certainly have to start with regular algebra
>all over again, and will probably only be able to take
>one course per semester. advice is appreciated.

Congratulations, monz!! Best of luck.

-Carl

Do it, Monz. Now that you have the motivation, you'll do much better
than you did in high school. In fact, I have a feeling you'll ace
these classes . . .

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> hey guys,
>
>
> i've finally decided to enroll in school again
> to study the math that i'm sorely lacking.
>
> i know that ultimately i want to take a course
> in linear algebra, and that Grassmann algebra in
> particular is something i want to be familiar with.
>
> the college catalog lists trigonometry and calculus
> as prerequisites for linear algebra, so this is going
> to be a long haul if i can stick with it. i nearly
> bombed out of algebra II in high school, and never
> studied math again after that ... except the bits
> and pieces i picked up as a tuning theorist.
>
> i feel like i'm missing out on too much new discovery
> here on tuning-math, and want to get up to speed.
>
> i haven't selected any particular classes yet.
> i will certainly have to start with regular algebra
> all over again, and will probably only be able to take
> one course per semester. advice is appreciated.
>
>
>
>
> -monz

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> hey guys,
>
>
> i've finally decided to enroll in school again
> to study the math that i'm sorely lacking.

Apparently it's never too late:

http://web.mit.edu/newsoffice/tt/1998/mar18/dabby.html

http://content.aip.org/CHAOEH/v6/i2/95_1.html

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> hey guys,
>
>
> i know that ultimately i want to take a course
> in linear algebra, and that Grassmann algebra in
> particular is something i want to be familiar with.
>
> the college catalog lists trigonometry and calculus
> as prerequisites for linear algebra, so this is going
> to be a long haul if i can stick with it.

I have a friend who got a degree in Business Admininstration and
then wanted to take some computer science classes for fun. They
burried him with a list of math prerequsites which I think he
worked hard on for maybe a year and a half and then burned out
without ever taking the computer classes he wanted.

Trigonometry and calculus are really irrelevant to linear algebra,
and Grassmann algebra is (i think) abstract algebra (groups, rings,
homomorphisms, etc) applied to linear algebra. In other words,
it is *much* harder, as in you get a bachelors degree in math and
then you take it in graduate school. Of course, you wouldn't need
the full force of it to follow most of the tuning-math discussions.

So maybe what you want is to get up to speed on basic algebra,
and then just go to the linear algebra class?

_jeff

jjensen142000 wrote:

> Trigonometry and calculus are really irrelevant to linear algebra,
> and Grassmann algebra is (i think) abstract algebra (groups, rings,
> homomorphisms, etc) applied to linear algebra. In other words,
> it is *much* harder, as in you get a bachelors degree in math and
> then you take it in graduate school. Of course, you wouldn't need
> the full force of it to follow most of the tuning-math discussions.

Trig and calculus are both handy to know, and do come up in tuning-math theory. So if they're pre-requisites, why not give them a try? It depends on how advanced the courses get. Easy trig and calculus are all you need.

Grassman algebra is based on wedge products. It's not that difficult. But it isn't that well known, so they'll only expect hard core mathematicians to learn it. Get basic algebra, and you should be able to learn it from the online materials, and questions here.

Also, you can avoid a lot of linear algebra if you know Grassman algebra. So choose your poison ...

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <graham@m...> wrote:

> Grassman algebra is based on wedge products. It's not that difficult.
> But it isn't that well known, so they'll only expect hard core
> mathematicians to learn it. Get basic algebra, and you should be able
> to learn it from the online materials, and questions here.
>
> Also, you can avoid a lot of linear algebra if you know Grassman
> algebra. So choose your poison ...

It's a subject normally taught to grad students which should be taught
to sophmores. In a linear algebra class, the sophmores will need to
learn the determinant. Textbook authors usually approach this from the
point of view of computing them by hand using Gaussian reduction,
which is pointless and does not advance your understanding much. They
should teach it from wedge products.