Arrange 4-Gon Figures: Find Descendants w/o Descendants

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SUMMARY

The discussion centers on the classification of 4-gon figures, specifically identifying descendants without further descendants. It establishes that a square is a descendant of a rectangle, which in turn is a descendant of a parallelogram. The key conclusion is that squares represent the subset of 4-gon figures that do not have any descendants, due to their unique symmetrical properties. The symmetry group of a square has an order of 8, distinguishing it from other quadrilaterals.

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  • Understanding of geometric classifications, specifically quadrilaterals
  • Familiarity with the concepts of subsets in set theory
  • Knowledge of symmetry groups and their orders
  • Basic understanding of the relationships between different polygon types
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  • Research the properties of symmetry groups in polygons
  • Explore the mathematical definitions of subsets and their applications in geometry
  • Study the hierarchy of quadrilaterals, focusing on rectangles and squares
  • Investigate the implications of symmetry in geometric classification
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Mathematicians, geometry enthusiasts, educators, and students studying polygon classifications and properties of quadrilaterals.

roni1
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If I arrange the 4-gon polygon by order as:
a rectangle is a descendant of parallelogram and a square is a descendant of rectangle.
What are the descendant that no have any descendants (in 4-gon figures)?
 
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What are the rules for determining descendants?
 
the property that the figure has like the father but you can say that the son have but so "fathers" (let call them father brothers) haven't.

square is the son of rectangle.

Not every rectangle can be a square,
But every square is a rectangle.
O.K.
The square is the son and the rectangle is the father. The brothers of the rectangle are rectangle that are not square.
 
Then I'd say a square is what your looking for; a square can only be a square.
 
roni said:
If I arrange the 4-gon polygon by order as:
a rectangle is a descendant of parallelogram and a square is a descendant of rectangle.
What are the descendant that no have any descendants (in 4-gon figures)?

Hi roni.

The mathematical term for what you call “descendants” is subsets. Thus, the set of all rectangles is a subset of the set of all parallelograms, and the set of all squares is a subset of the set of all rectangles.

The subset you’re looking for is the set of all squares because the square is the “most symmetrical” of all quadrilaterals – in the sense that its symmetry group has order 8 and no other quadrilateral has a symmetry group of the same or higher order.
 
Last edited:

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