Does Squaring Any Number Follow a Specific Pattern?

  • Context: High School 
  • Thread starter Thread starter DaveDem
  • Start date Start date
  • Tags Tags
    Teacher
Click For Summary

Discussion Overview

The discussion revolves around the mathematical pattern observed when squaring numbers and whether a specific method involving division and multiplication by two consistently yields correct results. Participants explore this concept through examples and reasoning, focusing on the implications of the operations involved.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes a method for squaring a number by dividing it by two and then multiplying by two, questioning if this always works.
  • Examples are provided by several participants, including squaring 16, 500, and 13, using the described method to demonstrate the process.
  • Another participant suggests trying the method with other numbers like 3, 5, or 7, providing an example with 7 to illustrate the approach.
  • There is a discussion about the nature of mathematical tricks and how they can obscure the underlying operations, with one participant noting that many tricks operate by hiding multiplication through division.
  • A participant references a famous rhyme to illustrate the concept of misleading appearances in mathematical reasoning.
  • Concerns are raised about the integrity of attributing ideas to teachers without proper acknowledgment, emphasizing the importance of honesty in discussions.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and acceptance of the method discussed, with no clear consensus on its validity or universality. The discussion remains unresolved regarding whether the method consistently applies to all numbers.

Contextual Notes

Some participants' examples may depend on specific interpretations of mathematical operations, and the effectiveness of the method may vary based on the numbers used. The discussion does not resolve the mathematical validity of the proposed method.

DaveDem
Messages
13
Reaction score
0
In math class my teacher said that if you take any base or A and square it that the answer is howmany times two goes into the base multiplied by the base times 2, does this always work?
 
Mathematics news on Phys.org
Can you give a couple of examples in different bases?
 
16 squared
16/2=8 16*2=32
32*8=256
 
500 squared
500/2=250 500*2=1000
250*1000=250000
 
13 squared
13/2=6.5 13*2=26
6.5*26=169
 
Have you tried it with other nunbers like 3, 5 or 7?

7x7=49

7/2=3.5

7*2=14

3.5 x 14 = 49

Like that?
 
Okay so basically you are dividing by two and then multiplying by two so the operations cancel out right?
 
yes exactly! i kinda came up with it but said it was my math teacher cause of the whole "if it doesn't come from someone with proof of knowledge we don't want to hear it" thing
 
Okay so you understand how it works now?
 
  • #10
Many of these math tricks work in a similar way by trying to hide the fact that you are multiplying by a factor early and then cancelling it out by dividing later on using valid math operations throughout the process.
 
  • #11
For example in your case you could say to add the number to itself instead of using times two to hide that fact and people may be fooled at first.
 
  • #13
there's no need to preface questions with my math teacher said unless they really said it. Its best to be honest rather than impune the integrity of your teacher for the sake of an answer.
 

Similar threads

  • · Replies 31 ·
2
Replies
31
Views
5K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 44 ·
2
Replies
44
Views
5K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 12 ·
Replies
12
Views
798
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K