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# Thread: Extending the range of calipers

1. Originally Posted by old_toolmaker
I did very well with geometry in high school. I was an A+ student. I struggled with Trigonometry though.
It wasn’t until I began my first year in Trade school the geometry really began to click for me. Suddenly I saw how it could be applied and used in the real world! I became an ace with geometry, so much so that I became the go to person if anyone had a geometry problem they deemed unsolvable. My ego became inflated! Then came CAD and now we were all on equal footing again. Everything seems to go full circle in the end. New technology replaces old an si goes evolution. Nothing is forever. Enjoy today!
The problem with CAD, and programs like it, is the fact that, while you can solve a particular problem, you learn nothing about math from it.

Mathematics is learned in a progression; each field builds on what was learned in the previous. Back when the schools actually taught useful material rather than woke psycho babble, the progression looked like

arithmetic
algebra
geometry
trigonometry
analytic geometry
calculus
advanced specialties, e.g. probability, statistics, matrix algebra, etc.

Once you introduce a tool like CAD, you eliminate the algebra and problem solving practice that you would get by following this progression.

2. ## The Following 2 Users Say Thank You to mklotz For This Useful Post:

old_toolmaker (Jun 13, 2021), volodar (Jun 13, 2021)

3. Originally Posted by WmRMeyers
There was a check for the digital calculators that involved multiplying the number 12345679 by a whole number multiple of 9 that was greater than 0 and less than 10. If the calculator gave a result that was the multiplier, supposedly the calculator was working correctly. 12345679 x 81 gave you 999999999, 12345679 x 18 gave you 222222222, etc. I doubt it checks all the functions even on a 4-function calculator, but I never ran into a calculator that didn't get the correct results. I was told that one of the spreadsheet programs, I think an early version of Excel didn't get it right, but my brain has fried a number of times since then. I barely remembered how to do this check myself. And the 2007 version does get it right.

Trust but verify!

Bill
In the days of calculators with seven segment digit displays, it was occasionally necessary to check that all the segments still functioned. This was done by dividing 80 by 9, which action would light every segment producing 8.888888...

This works because 1/9 is an infinite decimal whose expansion looks like 0.1111111... Multiplying that by 8 produces 0.8888888... To eliminate the leading zero, multiply by 80 to produce 8.888888...

The same trick can be used to produce a string of any desired digit. For example, 30/9 produces a string of 3s, 3.333333...

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Toolmaker51 (Jun 13, 2021)

5. Flashback, recalling the 80 x 9 = 8.888888 test. It wasn't verifying accuracy of calculation, but testing LED & LCD function to illuminate 100%. 8.888888 needs 49 elements. A random couple fizzle out, result changes a little, say [8.888889], or a lot [9.8888888]. No telling implications of that. Best thing about calculators, proving a calculation by running it again or changing operation etc is much quicker.
Goes without saying, that doesn't mean correct...
After writing, went back to alter font color; honoring those red displays, ala Texas Instruments. Mine would still work, isn't used anymore, just a little 'remember when?' thing. Whatever you do, make sure leaky 9v Duracell's aren't.

6. Originally Posted by Toolmaker51
Flashback, recalling the 80 x 9 = 8.888888 test. ...
80 / 9, not 80 * 9

Accuracy checks might include...

10 raised to the log(3) power - does it equal 3 ?

sin^2 + cos^2 should equal 1 for any angle

7. Whoops. X still isn't /, nor \; despite modest similarity

8. Originally Posted by Toolmaker51
Whoops. X still isn't /, nor \; despite modest similarity
Mathematicians seldom use 'x' to indicate multiplication because it's easily confused with the letter 'x' often used to denote the unknown in an equation. It is, however, used to indicate the cross product of two vectors.

Other options for multiplication include:

Simple juxtaposition ... ab - most frequently used
A raised dot between the two quantities - can't find a font that has that (also used to indicate the dot product of two vectors)
In coding, an asterisk ... a*b

The obelus (÷) is never used by mathematicians to indicate division. The forward slash (/) is preferred. The backslash (\) is sometimes used to indicate integer division where only the integerial part of the quotient is retained.

9. ## The Following User Says Thank You to mklotz For This Useful Post:

Toolmaker51 (Jun 13, 2021)

10. Originally Posted by mklotz
Mathematicians seldom use 'x' to indicate multiplication because it's easily confused with the letter 'x' often used to denote the unknown in an equation. It is, however, used to indicate the cross product of two vectors.

Other options for multiplication include:

Simple juxtaposition ... ab - most frequently used
A raised dot between the two quantities - can't find a font that has that (also used to indicate the dot product of two vectors)
In coding, an asterisk ... a*b

The obelus (÷) is never used by mathematicians to indicate division. The forward slash (/) is preferred. The backslash (\) is sometimes used to indicate integer division where only the integerial part of the quotient is retained.
Though I have taught mathematics, I have never claimed to be a mathematician. I assure you all of of that! I used the x for multiplication, which on computers is often indicated with an asterisk or *.

What I find interesting about this discussion is that I totally misapprehended the purpose of the test I described. Nor do I have any faintest clue as who originally told me about it.

Bill

11. Originally Posted by WmRMeyers
Though I have taught mathematics, I have never claimed to be a mathematician. I assure you all of of that! I used the x for multiplication, which on computers is often indicated with an asterisk or *.

What I find interesting about this discussion is that I totally misapprehended the purpose of the test I described. Nor do I have any faintest clue as who originally told me about it.

Bill
Not an issue. We have a zillion winkles up there; it's thought using them averts senility. Wrong isn't a tenth the problem gone is.

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