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::::If at the beginning of the section I had said "As a mathematical exercise" with no mention of the word "joke", or if I had simply omitted the introductory phrase and begun straight off with the statement "A circle can simultaneously present a square..." perhaps you would have been entertained with a serious-sounding proposition. I had fun with the visualization, but I was also quite serious. I repeat: Although I proposed a "solution" to the problem lightheartedly, it cannot be demonstrated to be either irrational or unreasonable. <br>Actually, I was holding back, because it can be achieved in 2 steps. ''Virtually'' bending the round edge of the circumference of a perfect circle (1) into four straight sections set at right angles (2) presents the same area in a square form as is bounded by the circle form. The shape has been changed but the 2-dimensional volume of the figure remains the same. This can be mentally visualized as a perfectly Euclidean plane figure using a perfect line without thickness. No mathematical proof is required. It is self-evident in its elegant simplicity.<br>Again, it can also be achieved physically in 4 steps as an illustration, just as perfect geometrical figures are illustrated with physical lines having visible thickness representing lines without thickness. Set a perfectly circular end of a cylinder on a flat table representing a Euclidean plane sprayed with a light mist of water (1). Tie a thin thread around it on the Euclidean plane (wet) surface of the table representing the line of circumference (2). Remove the cylinder, leaving the circle of thread unmoved (3). Arrange the circle of thread on the table into a square shape on the Euclidean plane of the (wet) table surface using an unmarked straightedge card or ruler to make the four sections of the thread straight (4). The circle of thread has been made square, enclosing the same area as the circle enclosed. <br>Again, inscribe a circle onto a flat surface with one of the points of a compass calipers (1). Close the points of the compass calipers and rotate the tiny interval of the closed points of the compass around the boundary of the circle point by point completing the whole circuit, counting the steps (2). Divide the number by four (3). With the straightedge as guide, using the same interval of the compass caliper points unchanged, rotate the tiny interval of the closed points of the compass calipers point by point along the straightedge on the flat surface, counting a distance equal to one-fourth of the circuit of the circumference of the circle, rotating the straightedge 90^o and repeating the operation three more times, giving four straight lengths adjoined at 90^o, describing a square enclosing virtually the same area as the circle (4).<br>This is fun, but it is at the same time a serious exercise. --[[User:Dataclarifier|Dataclarifier]] ([[User talk:Dataclarifier|talk]]) 00:52, 12 July 2019 (EDT)

::::If at the beginning of the section I had said "As a mathematical exercise" with no mention of the word "joke", or if I had simply omitted the introductory phrase and begun straight off with the statement "A circle can simultaneously present a square..." perhaps you would have been entertained with a serious-sounding proposition. I had fun with the visualization, but I was also quite serious. I repeat: Although I proposed a "solution" to the problem lightheartedly, it cannot be demonstrated to be either irrational or unreasonable. <br>Actually, I was holding back, because it can be achieved in 2 steps. ''Virtually'' bending the round edge of the circumference of a perfect circle (1) into four straight sections set at right angles (2) presents the same area in a square form as is bounded by the circle form. The shape has been changed but the 2-dimensional volume of the figure remains the same. This can be mentally visualized as a perfectly Euclidean plane figure using a perfect line without thickness. No mathematical proof is required. It is self-evident in its elegant simplicity.<br>Again, it can also be achieved physically in 4 steps as an illustration, just as perfect geometrical figures are illustrated with physical lines having visible thickness representing lines without thickness. Set a perfectly circular end of a cylinder on a flat table representing a Euclidean plane sprayed with a light mist of water (1). Tie a thin thread around it on the Euclidean plane (wet) surface of the table representing the line of circumference (2). Remove the cylinder, leaving the circle of thread unmoved (3). Arrange the circle of thread on the table into a square shape on the Euclidean plane of the (wet) table surface using an unmarked straightedge card or ruler to make the four sections of the thread straight (4). The circle of thread has been made square, enclosing the same area as the circle enclosed. <br>Again, inscribe a circle onto a flat surface with one of the points of a compass calipers (1). Close the points of the compass calipers and rotate the tiny interval of the closed points of the compass around the boundary of the circle point by point completing the whole circuit, counting the steps (2). Divide the number by four (3). With the straightedge as guide, using the same interval of the compass caliper points unchanged, rotate the tiny interval of the closed points of the compass calipers point by point along the straightedge on the flat surface, counting a distance equal to one-fourth of the circuit of the circumference of the circle, rotating the straightedge 90^o and repeating the operation three more times, giving four straight lengths adjoined at 90^o, describing a square enclosing virtually the same area as the circle (4).<br>This is fun, but it is at the same time a serious exercise. --[[User:Dataclarifier|Dataclarifier]] ([[User talk:Dataclarifier|talk]]) 00:52, 12 July 2019 (EDT)

::::I want to close with the fact that Paul Boisvert, professor of mathematics, Oakton Community College, Office: Room 2554 (Des Plaines Campus), claims to have a simple proof of [[Fermat's Last Theorem]] that even a child can understand. In the online article [https://www.oakton.edu/user/4/pboisver/fermat.html Simple Proof of Fermat's Last Theorem (oakton.edu)] he says, "Why, a child can follow the logic below." After reading it, determine for yourself if he is joking, making a mockery of a serious problem in mathematics, or if he is truly serious about his [[logic]]al proof, or if on the face of it he is perhaps doing both. I am inclined to hold to the last interpretation. --[[User:Dataclarifier|Dataclarifier]] ([[User talk:Dataclarifier|talk]]) 02:19, 12 July 2019 (EDT)

::::I want to close with the fact that Paul Boisvert, professor of mathematics, Oakton Community College, Office: Room 2554 (Des Plaines Campus), claims to have a simple proof of [[Fermat's Last Theorem]] that even a child can understand. In the online article [https://www.oakton.edu/user/4/pboisver/fermat.html '''A Simple Proof of Fermat's Last Theorem''' (oakton.edu)] he says, "Why, a child can follow the logic below." After reading it, determine for yourself if he is joking, making a mockery of a serious problem in mathematics, or if he is truly serious about his [[logic]]al proof, or if on the face of it he is perhaps doing both. I am inclined to hold to the last interpretation. --[[User:Dataclarifier|Dataclarifier]] ([[User talk:Dataclarifier|talk]]) 02:19, 12 July 2019 (EDT)