Mental Calculation as a Visual Construct

Mental Calculation, Mathematics, and Puzzles
1

I am noticing something odd…

When I attempt to calculate unfamiliar number…

83^2 for example.

When I see 83 written then…
6400+480+9 is obvious.

When it is not written down I find myself visualizing the digits 8 and 3 either seperately or as a group.

Now if I calculate with 83 in the center of my view I can almost but not quite see the answer by visualizing the numbers and using my memory for familiar transforms (283) rather than calculating them.

If I calculate 80 * 86 +3^2 which conceptually is a simpler problem I now find it significantly harder to envision the 2 entities with their 2 simple components interacting.

Onto the question?

Is this just a by product of a demented mind.

Is this a point in time effect and will the systems integrate more seamlessly with continued practice.

Is the whole trick to being fast and accurate with mental calculation as simple as reducing the load on the relatively stupid reasoning part of the brain and loading up the visual and memory elements to manipulate abstractions.?

Monkey wants a banana.

It’s curious either way. Memory Sports relies extremely heavily on our brilliant monkey brain.

Am I waving my arms in the right direction?

2

Think about it. You then need to remove the 83 from your minds eye and replace it with 80 and 86.
I think with practice this will improve.

3

For 83^2 specifically, another useful identity:

83 * 83 = (100-17) * (66 + 17) = 6600 + 17 * (100 -66 -17) = 6600 + 17^2 = 6600 + 289

So, basically you double the distance from 100, and then you add the square of the initial distance
since e.g. for every a<100,
a^2 = 100 * [100 - 2 *(100-a)]+ (100-a)^2

I’d personally find the ( 6600 + 289 ) operation , a bit faster than the
( 80 * 86 + 3^2 ) . But again, it’s a matter of taste. Both methods taste good. But memorizing all the first 100 squares, tastes even better.

Nodas

4

The beatings will continue until morale improves. I feel extremely lucky to have you two prodding me :).

Pick better algorithms and practice more… Got it.

This forum could use a few more posters to share in the relentless taunting. With a dozen or so this could be hugely entertaining.

5

For now just learn A LOT of algorithms and find out which ones work best in what circumstances.
A good drill is to do one calculation with all methods you know.

This works well when you work with longer numbers since the second calculation is helped by your memory of the previous numbers.