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

• MHB
• roni1
In summary, the subset of quadrilaterals that have no descendants in the 4-gon polygon are squares, due to their unique symmetry group and properties.
roni1
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)?

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.

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## 1. What is a 4-Gon figure?

A 4-Gon figure, also known as a quadrilateral, is a polygon with four sides and four angles.

## 2. How do you arrange 4-Gon figures?

To arrange 4-Gon figures, you can use various methods such as stacking, overlapping, or arranging them side by side. The arrangement will depend on the desired outcome and the specific figures being used.

## 3. What does "Find Descendants w/o Descendants" mean?

"Find Descendants w/o Descendants" refers to finding the descendants of a 4-Gon figure (i.e. other figures that can be created from it) without including any of its own descendants in the search.

## 4. Why is it important to find descendants without including its own descendants?

This is important because it allows for a more comprehensive analysis of the relationships between 4-Gon figures. By excluding a figure's own descendants, we can better understand its unique characteristics and how it relates to other figures in the same category.

## 5. What are some practical applications of arranging 4-Gon figures and finding their descendants?

Arranging 4-Gon figures and finding their descendants can be useful in various fields such as architecture, design, and mathematics. It can help in creating visually appealing patterns, understanding geometric relationships, and predicting the behavior of complex structures.

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