Lagrange multipliers and combinations of points

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SUMMARY

The discussion centers on the application of Lagrange multipliers in generating combinations of points in a three-dimensional space. Specifically, it addresses the misunderstanding of representing combinations with the notation (+-√2,+-1,+-√(2/3)), which actually denotes only two distinct points. The correct interpretation reveals that for y = +1 and y = -1, there are four combinations of x and z values, leading to a total of eight unique combinations when considering all sign variations.

PREREQUISITES
  • Understanding of Lagrange multipliers
  • Familiarity with three-dimensional coordinate systems
  • Basic knowledge of algebraic notation
  • Concept of combinations in mathematics
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  • Study the application of Lagrange multipliers in optimization problems
  • Explore three-dimensional geometry and its implications in mathematical modeling
  • Learn about combinatorial mathematics and its principles
  • Investigate the standard conventions for interpreting algebraic expressions in mathematics
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Mathematicians, students studying calculus and optimization, educators teaching algebraic concepts, and anyone interested in the geometric interpretation of mathematical combinations.

Miike012
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I was wondering how they got all the different combinations of points? Why can't they just put

(+-√2,+-1,+-√(2/3)) ?
 

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Miike012 said:
I was wondering how they got all the different combinations of points? Why can't they just put

(+-√2,+-1,+-√(2/3)) ?

When y = +1 there are two values of x and z, and when y = -1 there are two values of x and z, making a total of 8 combinations.

RGV
 
What you wrote, (+-√2,+-1,+-√(2/3)), would, by the standard conventions, be interpreted as two points, (+√2,+1,+√(2/3)) and (-√2,-1,-√(2/3))
 

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