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Cuchulainn
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Re: Back to Euclid

May 12th, 2023, 6:19 pm

solution
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triangle2.jpg
 
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Paul
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Re: Back to Euclid

May 12th, 2023, 9:09 pm

Looks like an answer from an LMH undergrad circa 1982.
 
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Cuchulainn
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Re: Back to Euclid

May 12th, 2023, 10:39 pm

Looks like an answer from an LMH undergrad circa 1982.
Lancaster Mennonite
Lady Margarget
?

My source is a friend of Mrs. C. She hated maths at school back then. We got talking about it (Euclid's book started flashing  early 60s.....) and it just stuck. I gave her the reference to Polya's How To book. She understood it pretty well. She now loves the beauty of mathematics.

For the record, I performed the same idea on LI 5 respondents

1 geometric .. correct 1st time
4 trig boys .. all incorrect on the first attempt and did not check their results

For me, a flashback to 1965. I have that Euclid book somewhere..
 
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Paul
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Re: Back to Euclid

May 13th, 2023, 6:15 am

Yes, Lady Margaret Hall. They always submitted the most beautiful answers, multi-coloured. 

There won't be full equality until, in the modern parlance, people without penises stop dotting their i's with tiny hearts.
 
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Cuchulainn
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Re: Back to Euclid

May 13th, 2023, 10:09 am

I wonder if 4 women took the trig approach then we would  probably have 4 correct answers. The guys on LI was over-confiident.
BTW do maths undergrads at Oxford do Euclid?? what about vector analysis?
It was taboo back then to mention the D (determinant) word. And Category Theory.

//

We wrote probably the first C++ library for a range of CAD/CAM/NC (e.g. AutoCAD) and graphics systems using design patterns etc.
Layering was super important due to complexity and range of requirements.
Templates ... quick prototypes use integer coordinates to fail fast.
We preferred the geometric approach to trig stuff. A real example at the time was finding the radical axis of 2 circles.
Exception handling in layered systems is awkward.

This leads us to an analysis of the Layers design pattern.
 
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Cuchulainn
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Re: Back to Euclid

May 13th, 2023, 10:23 am

The source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case. - Paul Halmos

In the beginning we worked on Medusa CAD (from Cambridge UK) in Fortran and expensive minicomputers to create some routines to interface to NC machines with metal flyin all over the place ) (basically early school level Cartesian geometry). 
This concrete example was the seed for that C++ library in AutoCAD, the latter becoming the Microsoft of the CAD world in the early 90s.
A 1/2 miillion guilders Medusa became a 40K AutoCAD solution on a 286 PC. The rest is history.
 
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Cuchulainn
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Re: Back to Euclid

May 14th, 2023, 8:43 pm

[$] x = \arctan(2 + \sqrt{3})  - 45 [$]

units: degrees
 
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Alan
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Re: Back to Euclid

June 23rd, 2023, 6:41 pm

[$] x = \arctan(2 + \sqrt{3})  - 45 [$]

units: degrees
   What is the lowest temperature ever recorded in Miami, Florida? 
   units: degrees F
 
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Cuchulainn
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Re: Back to Euclid

June 25th, 2023, 10:22 pm

[$] x = \arctan(2 + \sqrt{3})  - 45 [$]

units: degrees
   What is the lowest temperature ever recorded in Miami, Florida? 
   units: degrees F
Depends on the weather; if it's realy cold, they use Celsius, normally Fahrenheit 
e.g. High 90s,
say it is freezing 15 degrees  don't impress. So use C.
 
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Cuchulainn
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Re: Back to Euclid

June 26th, 2023, 10:28 am

I am wondering if the engineers of the disasterous Mars rover project used dimensional analysis..


https://en.wikipedia.org/wiki/Dimensional_analysis

I remember using it a while back in FEM.
 
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Alan
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Re: Back to Euclid

June 27th, 2023, 6:45 pm

[$] x = \arctan(2 + \sqrt{3})  - 45 [$]

units: degrees
   What is the lowest temperature ever recorded in Miami, Florida? 
   units: degrees F
Depends on the weather; if it's realy cold, they use Celsius, normally Fahrenheit 
e.g. High 90s,
say it is freezing 15 degrees  don't impress. So use C.
The correct response is: congratulations -- you solved the puzzle.
 
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Cuchulainn
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Re: Back to Euclid

July 2nd, 2023, 7:18 pm


   What is the lowest temperature ever recorded in Miami, Florida? 
   units: degrees F
Depends on the weather; if it's realy cold, they use Celsius, normally Fahrenheit 
e.g. High 90s,
say it is freezing 15 degrees  don't impress. So use C.
The correct response is: congratulations -- you solved the puzzle.
This is not my solution! It took 5 people 3-4 attempts on LI to get it right.