
04142020, 06:59 PM #81
You didn't give any answer other than "Next time" and a link to an area calculator with *irrelevant to the question* sample formulae. If I missed it, quote your answer. And thanks for the formula that I already used in my first reply. I'm starting to see why everyone thinks you're a jerk.



04142020, 07:03 PM #82
One can’t xsplane math stuff with Xjoniqirrets (Martian practical 6th dimensional hyperbolic geometry in gradient relationship to algebraic topology.) at a 6th grade level.
likely it would be easier to teach a gold fish to read.
(I know we don't have gold fish here on Mars, I just used that because most know what a gold fish is.}
Post 76 keep it simple.
Buck

04142020, 07:40 PM #83
"Set theory is the very most basic & therefore abstract underpinning of mathematics."
I am sorry, but I can not let that statement stand without at least a comment. I have a background that includes mathematics and I feel and have always felt that counting things is the "abstract underpinning of mathematics" as well as the practical basis or underpinning of mathematics. In other words,
COUNTING ON YOUR FINGERS.
Mathematics began with counting things and counting things started with counting on your fingers. The idea that seven fingers can represent an equal number of sheep or birds or arrow heads or whatever is a very deep and profound idea. This is not trivial. Likewise, a group of stones or twigs or marks in the ground can be used instead of fingers. Etc. This is a process of abstracting the idea of numbers and even cave men did it.
Abstracting the idea of numbers is the indisputable underpinning of mathematics and, IMHO, should be in the first chapter of every book on math. or at least in the first, introductory book on each branch of math. And totally contrary to the feelings of my own grammar school teachers, it should be illustrated with counting with fingers. This would communicate the very basis of mathematics. THE VERY BASIS!
Set theory is a late development in mathematics. Mathematics existed for centuries, for hundreds of centuries, for most of recorded human history without any inkling of set theory. Set theory is only, I said ONLY, one of the latest branches of math. I have nothing against set theory, but it was never the underpinning of math. If I were a betting man and if I could find a bookie to take the bet, I would get rich by betting that some new and presently unknown branch of math will one day supplant set theory as "the underpinning of math". That is totally inevitable. Of course I may have to have one of my descendants collect on that bet. But it is a very safe bet.
Now, set theory may be a good start for a college program in mathematics, but it will never be the first starting point in their overall training. That goes back to what they are exposed to in grammar school and that or at least what counts in that is learning how to count and how to do basic manipulations with those counting numbers: addition, subtraction, multiplication, and division. That is where all math training really starts, even if an abstract idea like set theory is forced upon first grade students who can never really understand it. In practice, they get absolutely nothing from that exposure at the age of six or seven. Nothing. Just ask a person who finished eighth grade to explain set theory and see what you get. Gibberish, at best. More likely a blank stare.

04142020, 07:51 PM #84
While that is of course correct, we would have gotten dinged on an exam if presented that way.
Rt = ratio of volume
V2 = volume of large ball
V1 = volume of small ball
r2 = radius of large ball
r1 = radius of small ball
Rt = V2 / V1 = 4/3π•r2³ / 4/3π•r1³ = r2³ / r1³
Correct answer: Rt = r2³ / r1³
(not picking on you or anyone, I'm just inf'ncredibly bored right now while waiting for an EDM cut to finish so I can continue on with my real misery ... )

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04152020, 11:20 AM #85
Some are so overthinking this.
So I thought an illustration would be in order. If you rotate a copy of the triangle 180 degrees and join them at the longest dimension you get a parallelogram.
The area of a parallelogram = BASE times HEIGHT or in this case 12 x 6, which equals 72.
Since the parallelogram consists of two triangles of identical size and shape the are of each one is 1/2 that of the parallelogram which in this case is 36.
Yes, the horizontal lines are skewed. This happened when I went from a vector based drawing to a raster based image. Close enough for illustrating a math problem.


04152020, 11:34 AM #86


04152020, 12:05 PM #87
Counting is NOT the basis of mathematics because you need to define what you're counting, how you're going to do it before starting. From a mathematicians point of view, counting and measuring get you nowhere because they don't help prove any of the properties of the things being manipulated.
Example: there is a well known formula for the sum of the first N integers. You can spend the rest of your life counting and demonstrating and never find a counter example, but that is not a proof. The proof comes from using induction on the natural numbers which is one of Peano's axioms. I know it's modern math to the ancient Egyptians, but Peano's axioms were published about 130 years ago.

04152020, 01:26 PM #88
I don't agree, not necessarily. One problem with math, and mathematicians, is it can lead to 'too much thinking'. That is to say, SOMETIMES a lot of thought is important and useful, but sometimes it isn't. Math provides the very clear opportunity to overthink; an opportunity that many people are unable to avoid.
Counting probably is the basis of math...it could be argued that all of higher math  calculus, trig, algebra etc.  is only there to allow counting to happen. They allow us to count past 20 using our fingers and toes (or 21 if your are in the bath tub). They allow us to count when 4 or 5 variables are changing all at the same time. Or being multiplied or divided. But it's still counting.
If you are a caveman, and have 5 dead rabbits you've killed, all the integers in the world are totally useless. But it's very useful to count how many rabbits you have and how many mouths you have to feed.

04152020, 01:55 PM #89


04152020, 01:57 PM #90
There are only 10 kinds of people in the world.
Those who understand binary and those who don't.

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04152020, 01:59 PM #91

04152020, 02:07 PM #92

04152020, 02:41 PM #93

04152020, 03:12 PM #94
Would things be different if we did't have 10 fingers?
Base eight and base 12 come to mind, base eight for just using fingers no thumbs and base 12 if we had an extra digit on each hand.

04152020, 03:35 PM #95


04152020, 03:39 PM #96
Actually, not what was claimed, which was running en masse off a cliff when faced with overpopulation. It was revealed some years ago that the filmmaker had the animal wrangler PUSH them towards the edge of the cliff with a piece of plywood just offcamera.
Oh the Humanity! Poor little innocent lemmings pushed to their death so a filmmaker could push his population control agenda.

04152020, 03:40 PM #97

04152020, 04:18 PM #98
There's an awful lot of symmetry in '10', regardless of how many finger we have. Among others, it is far easier for the mind to divide, multiply etc in 10's than it would be in 9's or some other number. It's also the logical place to 'start over' when counting because it's the first combination of single digit numbers you hit.

04152020, 04:21 PM #99

04152020, 06:03 PM #100
Actually base 12 makes a hell of a lot of sense. It can be divided by 1, 2, 3, 4, 6,and 12. Base ten can only be divided by 1, 2 5, and 10. Easier to divide up inheritances when you have 1, 2, 3, 4...heirs. Two more symbols are easy enough to remember. If you were raised using base 12 from birth you would probably think base 10 is weird.

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