1(square)=1 but ,2 square not equal to 2

  • Context: High School 
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Discussion Overview

The discussion revolves around the mathematical concept of squaring numbers, specifically examining why 1 squared equals 1 while 2 squared does not equal 2. Participants explore logical interpretations and implications of these mathematical operations.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asserts that 1 x 1 equals 1, while 2 x 2 does not equal 2, seeking clarification on this logical discrepancy.
  • Another participant points out that 2 x 2 equals 4, not 2, suggesting a misunderstanding of the operations involved.
  • A different participant explains that four 1x1 squares can fit into one 2x2 square, hinting at a geometric interpretation.
  • One post introduces historical context, mentioning that ancient Greeks recognized the distinction between these operations and shifted their focus from algebra to geometry.
  • Another participant humorously notes that while 3 ft x 3 ft equals 1 square yard, the concept becomes more complex with larger dimensions, like 50 ft x 100 ft equating to a rectangular yard.
  • One participant suggests that 2 x 2 can be viewed as equivalent to 2 + 2, contrasting it with 1 x 1 being simply 1 equals 1.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of squaring numbers, with some providing explanations while others question the initial premise. There is no consensus on the underlying logic or the implications of these mathematical operations.

Contextual Notes

Some claims rely on interpretations of mathematical operations that may not be universally accepted, and there are references to historical perspectives that are not elaborated upon. The discussion includes playful and speculative elements that may not adhere to formal mathematical definitions.

creater
hi all,
it may sound silly .. but when we look at this logically

1 X 1= 1.. that is 1(square) is 1

but

2 X 2 not = 2

i don't understand why?

please help me understand this
 
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Really?

Likely its because 2x2= 4, not 2.

I sense Troll.
 
Because you can fit four 1x1 squares into one 2x2 square.
 
creater said:
1 X 1= 1 ... but 2 X 2 not = 2
You left out 0 x 0 = 0. In fact, a little known fact is the fact that the ancient Greeks were aware of the fact that 2 x 2 not = 2 and for this reason, abandoned algebra to the Arabs while studying geometry instead. When young Gauss was in kindergarten, he noticed that [itex]\infty[/itex]x[itex]\infty = \infty[/itex]. This appeased the Greeks somewhat and now they study algebra too. If I'm not mistaken, the Arabs also study geometry, so all's well with the world. Don't upset the apple cart.
 
creater said:
hi all,
it may sound silly .. but when we look at this logically

1 X 1= 1.. that is 1(square) is 1

but

2 X 2 not = 2

i don't understand why?

please help me understand this

Yet 3 ft x 3 ft = 1 square yard!

And, even more bizarre, 50 ft x 100 ft = 1 rectangular yard. (At least if your neighborhood is flat. If your yard is sloped, I'm scared to even try to figure out what 50 ft x 100 ft equals.)
 
creater said:
hi all,
it may sound silly .. but when we look at this logically

1 X 1= 1.. that is 1(square) is 1

but

2 X 2 not = 2

i don't understand why?

please help me understand this

Because 2 x 2 is equivalent to saying 2 + 2 whereas 1 x 1 is equivalent to saying 1=1
 

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