OT- Triangle Area Question / 6th Grade Math - Page 5
Close
Login to Your Account
Page 5 of 10 FirstFirst ... 34567 ... LastLast
Results 81 to 100 of 183
  1. #81
    Join Date
    Mar 2005
    Country
    UNITED STATES
    State/Province
    Indiana
    Posts
    4,757
    Post Thanks / Like
    Likes (Given)
    1255
    Likes (Received)
    1189

    Default

    Quote Originally Posted by Gordon B. Clarke View Post
    What's your problem? I gave the answer and the correct formula many posts ago.

    Are you sure you're readng my posts? Maybe time for new glasses or improving your reading ability?
    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.

  2. #82
    Join Date
    Jun 2012
    Country
    UNITED STATES
    State/Province
    Michigan
    Posts
    11,636
    Post Thanks / Like
    Likes (Given)
    3977
    Likes (Received)
    4139

    Default

    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

  3. #83
    Join Date
    Nov 2003
    Country
    UNITED STATES
    State/Province
    Texas
    Posts
    5,406
    Post Thanks / Like
    Likes (Given)
    188
    Likes (Received)
    1803

    Default

    "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.



    Quote Originally Posted by MrStretch View Post
    Set theory is the right place to start for training a mathematician, not a human calculator which is what math education is geared towards. Set theory is the very most basic & therefore abstract underpinning of mathematics.
    Cutting a piece of paper and rearranging the pieces is not a proof but rather a demonstration of a particular case.

  4. #84
    Join Date
    Aug 2005
    Location
    CT
    Posts
    7,960
    Post Thanks / Like
    Likes (Given)
    352
    Likes (Received)
    1959

    Default

    Quote Originally Posted by eKretz View Post

    For the 2" steel ball, 4/3π•r³ = 4.1888 in³

    For the 1" steel ball, 4/3π•r³ = 0.5236 in³

    4.1888 in³ ÷ 0.5236 in³ = 8.


    .
    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 in-f'n-credibly bored right now while waiting for an EDM cut to finish so I can continue on with my real misery ... )

  5. Likes Bobw liked this post
  6. #85
    Join Date
    Nov 2013
    Location
    Eastern Massachusetts, USA
    Posts
    5,474
    Post Thanks / Like
    Likes (Given)
    5197
    Likes (Received)
    5241

    Default

    Some are so over-thinking 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.

    triangle-area.jpg

    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.

  7. #86
    Join Date
    Feb 2014
    Location
    FL
    Posts
    3,433
    Post Thanks / Like
    Likes (Given)
    11703
    Likes (Received)
    3930

    Default

    Quote Originally Posted by ekretz View Post
    i'm starting to see why everyone thinks you're a jerk.

    JUST NOW??

    It was THIS thread that did it?

  8. Likes DrHook, camscan, eKretz, Screwmachine liked this post
  9. #87
    Join Date
    Mar 2017
    Country
    UNITED STATES
    State/Province
    Pennsylvania
    Posts
    233
    Post Thanks / Like
    Likes (Given)
    2
    Likes (Received)
    104

    Default

    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.

  10. #88
    Join Date
    Jan 2005
    Location
    Houston
    Posts
    6,245
    Post Thanks / Like
    Likes (Given)
    788
    Likes (Received)
    3007

    Default

    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.

  11. #89
    Join Date
    May 2010
    Country
    DENMARK
    Posts
    3,719
    Post Thanks / Like
    Likes (Given)
    4080
    Likes (Received)
    12727

    Default

    Quote Originally Posted by TeachMePlease View Post
    JUST NOW??

    It was THIS thread that did it?
    LOL I regard it a "follow" thing the same as sheep and lemmings. They do what they do and don't know why.

    It obviously doesn't take much to get some upset and even less to keep them busy.

  12. #90
    Join Date
    Sep 2015
    Country
    UNITED STATES
    State/Province
    Ohio
    Posts
    1,299
    Post Thanks / Like
    Likes (Given)
    860
    Likes (Received)
    1301

    Default

    There are only 10 kinds of people in the world.
    Those who understand binary and those who don't.

  13. Likes SBLatheman, Scottl liked this post
  14. #91
    Join Date
    May 2010
    Country
    DENMARK
    Posts
    3,719
    Post Thanks / Like
    Likes (Given)
    4080
    Likes (Received)
    12727

    Default

    Quote Originally Posted by GregSY View Post
    One problem with math, and mathematicians, is it can lead to 'too much thinking'.
    Would things be different if we did't have 10 fingers?

  15. #92
    Join Date
    Jan 2014
    Location
    Temecula, Ca
    Posts
    3,276
    Post Thanks / Like
    Likes (Given)
    1396
    Likes (Received)
    4259

    Default

    Quote Originally Posted by Gordon B. Clarke View Post
    Would things be different if we did't have 10 fingers?
    10? Who has 10?

  16. #93
    Join Date
    Sep 2011
    Location
    Posts
    1,793
    Post Thanks / Like
    Likes (Given)
    103
    Likes (Received)
    73

    Default

    Quote Originally Posted by Gordon B. Clarke View Post
    LOL I regard it a "follow" thing the same as sheep and lemmings. They do what they do and don't know why.

    It obviously doesn't take much to get some upset and even less to keep them busy.
    So what do lemmings do!

  17. #94
    Join Date
    Sep 2011
    Location
    Southern Indiana USA
    Posts
    167
    Post Thanks / Like
    Likes (Given)
    18
    Likes (Received)
    79

    Default

    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.

  18. #95
    Join Date
    Feb 2005
    Location
    Hatch, NM Chile capital of the WORLD
    Posts
    9,262
    Post Thanks / Like
    Likes (Given)
    14980
    Likes (Received)
    11104

    Default

    Quote Originally Posted by Larry Dickman View Post
    10? Who STILL has 10?
    Says the shop teacher.

  19. #96
    Join Date
    Nov 2013
    Location
    Eastern Massachusetts, USA
    Posts
    5,474
    Post Thanks / Like
    Likes (Given)
    5197
    Likes (Received)
    5241

    Default

    Quote Originally Posted by camscan View Post
    So what do lemmings do!
    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 off-camera.

    Oh the Humanity! Poor little innocent lemmings pushed to their death so a filmmaker could push his population control agenda.

  20. #97
    Join Date
    Nov 2013
    Location
    Eastern Massachusetts, USA
    Posts
    5,474
    Post Thanks / Like
    Likes (Given)
    5197
    Likes (Received)
    5241

    Default

    Quote Originally Posted by theperfessor View Post
    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.
    And base 20 if we hadn't started wearing shoes?

  21. #98
    Join Date
    Jan 2005
    Location
    Houston
    Posts
    6,245
    Post Thanks / Like
    Likes (Given)
    788
    Likes (Received)
    3007

    Default

    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.

  22. #99
    Join Date
    Jan 2014
    Location
    Temecula, Ca
    Posts
    3,276
    Post Thanks / Like
    Likes (Given)
    1396
    Likes (Received)
    4259

    Default

    Quote Originally Posted by Scottl View Post
    And base 20 if we hadn't started wearing shoes?
    I was thinkin half the population could go to 21

  23. #100
    Join Date
    Sep 2011
    Location
    Southern Indiana USA
    Posts
    167
    Post Thanks / Like
    Likes (Given)
    18
    Likes (Received)
    79

    Default

    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.

  24. Likes Bobw liked this post

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •