Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; if and only if there is a curve connecting points before, there is a curve connecting those points after) vs. not so.

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points, and where and only where there are curves connecting points before there are curves connecting those points after) vs. not so.

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points, and where and only where there are paths connecting points before there are paths connecting those points after) vs. not so.

Left examples are topologically homeomorphic figures.

For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points and the same pairs of these points have a path connecting them) vs. not so.

Left examples are topologically homeomorphic figures.

For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square.

Figures can be transformed into one another by smooth stretching (intersection points stay constant; paths connecting those points remain) vs. not so.

Figures can be transformed into one another by smooth stretching (intersection points stay constant; paths connecting those points remain) versus not so.

The figures are topologically homeomorphic.

For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square.

Aaron David Fairbanks

This is a very specific parsing of the world. It is likely the world would instead be parsed as BP803. BP pages listing this as their world should list that world also as an alternative option.

This is a very specific parsing of the world. It is likely the world would instead be parsed as BP803. BP pages listing this world should list that world also as an alternative option.

Bongard Problems with "world" one black or outline triangle or quadrilateral vs. other Bongard Problems.

This is a very specific parsing of the world. It is likely the world would instead be parsed as BP803. Usually BP pages listing this world list that world also as an alternative option.

Aaron David Fairbanks