@anon: Thanks for the feedback and support!
Mathematics is my soul.
Hi,
Thanks for saving my life , by the way can you update this post with different meaning of division please i cant really get it.
Hi Satheesh, thanks for the note. I try to see division as just a type of multiplication. I.e., instead of “divide by 3” think “multiply by 1/3”. Then, division just becomes a different type of scaling [which will normally make you smaller… but if you divide by 1/2, you make yourself larger].
Sateesh, I love the explanations that you and the other commentators have offered. I used many of these when I was teaching in the inner city, where a significant minority of our students used fingerplay for addition and subtraction, and even for multiplication (they just left division questions blank).
I am blogging for a site whose philosophy is that it you kick math facts out of the prefrontal cortex and down to the automated recall areas of the brain like the parietal sulcus, the higher brain is available for conceptual work. At http://www.mathnook.com/blog, you’ll find an article with hot links to the brain science articles. I’m curious what you think of a confluence of conceptual and automated thinking. I think it’s like strategic planning meeting operations in a company.
Did you really mean in the email you sent, that “The opposite of the opposite of 1 is 1”? Or did you mean “The opposite of the opposite of -1 is 1”. Wasn’t sure about that part.
Hi Brett, great question – yep, it was meant to be 1.
“The opposite of 1” is -1. And if we take the opposite again (“the opposite of the opposite”) we get the original back. Hope that helps!
Really like your weekly emails. I am doing some work with R and I was curious to predict how many distance results would the dist() function produce. I started by summing: (n-1) + (n-2) + (n-3) … (n- (n-1)). Then using the insights presented in newsletter: “A quick intro to intuitive learning” I arrived at: (n-1) * n / 2 gives the answer. the dist() function compare each element with every other element but removes the duplicates. For a set of 4 {1,2,3,4} there would be 6 distances generated.
> a
[1] 1 2 3 4
> dist(a)
1 2 3
2 1
3 2 1
4 3 2 1
> length(dist(a))
[1] 6 ## Result from R
Using my new formula: 4 * (4-1) / 2 = 6. ## It works
Now, for 40 elements:
> b = 1:40 # create a set of 40 elements 1 to 40
> length(dist(b))
[1] 780 ## Result from R
Using my new formula: 40 * (40 - 1) /2 = 780 ## Works again!
This really great after just reading the first news letter… so thanks and keep them coming!!!
Dear Khalid,
I am 45. I am an engineer,
But I never really understood some basic concepts in maths, like multiplication of negative number by a negative number. I used to memorize many concepts, which ultimately have been internalized. But there was always a kind of vacuum, a kind of unease.
Your ideas and explanations are great. It really opened a different perspective not only in understanding maths, but many other things in life.
I feel the site on calculus needs some rework.
Keep it up Khalid keep it up.
I’m a very basic guy and I ask myself why on earth would I want to transform a random number in the range 0 -1 to the range 5 - 10. Without any concreteness this is meaningless.
Love the rest of this article though.
Thank you for sharing your knowledge for free.
Dear Khalid!
we can say adding numbers were one dimensional…
multiplying numbers were more than one dimension.
for ex: 2x3=6…invariably we are representing a AREA(lengthxbreadth)
for ex:2x3x2=12 …we are representing a volume (length x breadth x depth) isn’t it?..
but ex:2x3x2x4=48 …still we are referring 3 dimensions, because we are living in a 3 dimensional space…
after relativity …time as fourth dimension…mingled as space-time continuum…
so up to square root and cube root I can relate intuitively …beyond that it is beyond the scope of my brain…