Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On 07/01/2014 02:56 PM, Jim Thompson wrote:
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson

Move one of the arctans to the other side of the equation, take the
tangent of both sides using the formula for tan(a+b), and solve it
algebraically.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

On Tue, 01 Jul 2014 15:30:18 -0400, Phil Hobbs
wrote:

On 07/01/2014 02:56 PM, Jim Thompson wrote:
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson

Move one of the arctans to the other side of the equation, take the
tangent of both sides using the formula for tan(a+b), and solve it
algebraically.

Cheers

Phil Hobbs

The arctans are on the one side.

As I see it, applying TAN to both sides gives

TAN(THETA) = TAN(arctan1 + arctan2)

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On 07/01/2014 03:55 PM, Jim Thompson wrote:
On Tue, 01 Jul 2014 15:30:18 -0400, Phil Hobbs
wrote:

On 07/01/2014 02:56 PM, Jim Thompson wrote:
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson

Move one of the arctans to the other side of the equation, take the
tangent of both sides using the formula for tan(a+b), and solve it
algebraically.

Cheers

Phil Hobbs

The arctans are on the one side.

As I see it, applying TAN to both sides gives

TAN(THETA) = TAN(arctan1 + arctan2)

...Jim Thompson


There are different ways to do it, but you'll need the tan(a+b) formula.
That'll make it an algebraic equation rather than a transcendental one.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

On Tue, 01 Jul 2014 16:57:13 -0400, Phil Hobbs
wrote:

On 07/01/2014 03:55 PM, Jim Thompson wrote:
On Tue, 01 Jul 2014 15:30:18 -0400, Phil Hobbs
wrote:

On 07/01/2014 02:56 PM, Jim Thompson wrote:
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson

Move one of the arctans to the other side of the equation, take the
tangent of both sides using the formula for tan(a+b), and solve it
algebraically.

Cheers

Phil Hobbs

The arctans are on the one side.

As I see it, applying TAN to both sides gives

TAN(THETA) = TAN(arctan1 + arctan2)

...Jim Thompson


There are different ways to do it, but you'll need the tan(a+b) formula.
That'll make it an algebraic equation rather than a transcendental one.

Cheers

Phil Hobbs

A _messy_ Algebraic equation :-)

Oooops! I just realized the advantage of your approach... ding-dong
:-|

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

Not sure, but whatever it is, it's literally ahead of its time. Four
years? Getting a bit presumptuous in your old age there.

Tim

--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

"Jim Thompson" wrote
in message ...
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On Tue, 1 Jul 2014 16:16:08 -0500, "Tim Williams"
wrote:

Not sure, but whatever it is, it's literally ahead of its time. Four
years? Getting a bit presumptuous in your old age there.

Tim

Aarrrgh :-(

Knock on wood, I don't seem to be as frail as my father was when he
was 74, and he made it to 90.

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

"Jim Thompson" wrote in
message ...
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

tan(a) + tan(b)
tan(a+b) = ----------------
1 - tan(a)*tan(b)

I think your only hope is a numerical approach. I suggest you state the
problem in the form: a = fa(x, y, p), b = fb(x, y, p) and post your query on
the SciPy newsgroup: http://scipy-central.org/.

On Tue, 1 Jul 2014 19:02:04 -0700, "garyr" wrote:


"Jim Thompson" wrote in
message ...
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

tan(a) + tan(b)
tan(a+b) = ----------------
1 - tan(a)*tan(b)

I think your only hope is a numerical approach. I suggest you state the
problem in the form: a = fa(x, y, p), b = fb(x, y, p) and post your query on
the SciPy newsgroup: http://scipy-central.org/.




I thinks Hobbs' move satisfies the Algebra. I'll report back later...
this is all about behavioral modeling/curve fitting.

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On Tue, 01 Jul 2014 11:56:27 -0700, Jim Thompson
wrote:

Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?


This is too messy to attempt an algebraic solution, particularly since
you're starting with transcendental functions. Use numerical methods
to find a solution. If you're not prepared to do it discretely, Matlab
or Mathcad might be able to solve it for you.

On 02/07/2014 03:36, Jim Thompson wrote:
On Tue, 1 Jul 2014 19:02:04 -0700, "garyr" wrote:


"Jim Thompson" wrote in
message ...
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

tan(a) + tan(b)
tan(a+b) = ----------------
1 - tan(a)*tan(b)

I think your only hope is a numerical approach. I suggest you state the
problem in the form: a = fa(x, y, p), b = fb(x, y, p) and post your query on
the SciPy newsgroup: http://scipy-central.org/.




I thinks Hobbs' move satisfies the Algebra. I'll report back later...
this is all about behavioral modeling/curve fitting.

...Jim Thompson

A few small substitutions will help you see the wood for the trees.

If I have read it right then the following will turn it into a
recognisable quadratic form.

Let
t = tan(theta)
x = Xw
y = 1-Yw^2
p = P/w

with the tan formula above simplifying and then later z = x/y to get a
quadratic form which subject to algebra slips I get to be :

(1-pt)z^2 + 2(p+t)z - 1 + pt = 0

Hence an expression for z = x/y as a function of p

Quick and dirty approx starting solution from
sqrt(1+x) = 1 + 2x/(4+x) x=1

Numerical might be less hassle than close form YMMV

--
Regards,
Martin Brown