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7 replaced http://puzzling.stackexchange.com/ with https://puzzling.stackexchange.com/

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intentanother puzzle with the original intent.)

Reflexivity — When the self refers to itself. Above is a simple polygonal region divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   If 2 copies are removed, the remaining polygonal region is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygonal region is geometrically similar, without reflection, to what remains if 2 or more component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Reflection is not in play.   Each copy size occurs only once.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intent.)

Reflexivity — When the self refers to itself. Above is a simple polygonal region divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   If 2 copies are removed, the remaining polygonal region is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygonal region is geometrically similar, without reflection, to what remains if 2 or more component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Reflection is not in play.   Each copy size occurs only once.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intent.)

Reflexivity — When the self refers to itself. Above is a simple polygonal region divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   If 2 copies are removed, the remaining polygonal region is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygonal region is geometrically similar, without reflection, to what remains if 2 or more component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Reflection is not in play.   Each copy size occurs only once.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.

6 title change, "polygon" --> "polygonal region," retrofit (again) to match only solution and allow for new puzzle

# Infinitely Unreflected infinitely simple polygon solipsismreflexivity

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intent.)

SolipsismReflexivityTheWhen the self is all that can be knownrefers to existitself.  Above is a simple polygonpolygonal region divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   If 2 copies are removed, the remaining polygonal region is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, with a maximum successive-size ratio as close as possible to 1where the original polygonal region is geometrically similar, without reflection, to what remains if 2 or more component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Reflection is not in play.   Each copy size occurs only once.   Reflection is allowed.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or most commonsmallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.   A neat solution with only right angles and a maximum ratio less than 1.3 is known at pose time.

# Infinitely simple polygon solipsism

SolipsismThe self is all that can be known to exist. Above is a simple polygon divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, with a maximum successive-size ratio as close as possible to 1?

Each copy size occurs only once.   Reflection is allowed.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or most common, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.   A neat solution with only right angles and a maximum ratio less than 1.3 is known at pose time.

# Unreflected infinitely simple polygon reflexivity

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intent.)

ReflexivityWhen the self refers to itself. Above is a simple polygonal region divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   If 2 copies are removed, the remaining polygonal region is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygonal region is geometrically similar, without reflection, to what remains if 2 or more component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Reflection is not in play.   Each copy size occurs only once.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.

5 Rollback to Revision 3

(This was retrofitted to more narrowly match the only solution yet and to allow for another more-strictly stated puzzle.)

Solipsism — The self is all that can be known to exist.  Above is a simple polygon divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   After the two largest copies are removed, the remaining polygon is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygon is geometrically similar to what remains after the two largest component copies are removedwith a maximum successive-size ratio as close as possible to 1?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Each copy size occurs only once.   Reflection is allowed.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallestmost common, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.   A neat solution with only right angles and a maximum ratio less than 1.3 is known at pose time.

(This was retrofitted to more narrowly match the only solution yet and to allow for another more-strictly stated puzzle.)

Solipsism — The self is all that can be known to exist. Above is a simple polygon divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).   After the two largest copies are removed, the remaining polygon is a scaled-down version of the original.

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, where the original polygon is geometrically similar to what remains after the two largest component copies are removed?

The open-ended goal is a maximum successive-size ratio as close as possible to 1.

Each copy size occurs only once.   Reflection is allowed.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or smallest, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.   A neat solution with only right angles and a maximum ratio less than 1.3 is known at pose time.

Solipsism — The self is all that can be known to exist. Above is a simple polygon divided into infinitely many different-sized copies of itself.   Each copy is √2 = 1.414... times as large as the next smaller one (in terms of linear scale, not area).

Can you find another simple polygon that has 4 or more sides and can be divided into infinitely many different-sized copies of itself, with a maximum successive-size ratio as close as possible to 1?

Each copy size occurs only once.   Reflection is allowed.   Polygons in this puzzle have finitely many vertices.   Note that the goal is to minimize the maximum, not average or most common, ratio between any two successively sized copies.   The large composite polygon is not included in these ratios.   A neat solution with only right angles and a maximum ratio less than 1.3 is known at pose time.

4 retrofit statement to match the lone answer and allow for a new puzzle
3 clarify that size is linear scale, use clearer example picture
2 clarify that each size is one of a kind, add [tag:geometry]
1