Given three segments OP1,OP2,OP3 in a plane ω, which are not contained in a line, we find a simple necessary and sufficient condition for the existence of two distinct ellipses centered at O and circumscribing the three ellipses having as conjugate semi-diameters the pairs (OP1,OP2), (OP2,OP3) and (OP3,OP1). We prove this result by showing that it is equivalent to the existence of a secondary Pohlke’s projection closely related to the (always existing) projection given by Pohlke’s fundamental theorem of oblique axonometry.
A note on a secondary Pohlke’s projection
MANFRIN, RENATO
2021-01-01
Abstract
Given three segments OP1,OP2,OP3 in a plane ω, which are not contained in a line, we find a simple necessary and sufficient condition for the existence of two distinct ellipses centered at O and circumscribing the three ellipses having as conjugate semi-diameters the pairs (OP1,OP2), (OP2,OP3) and (OP3,OP1). We prove this result by showing that it is equivalent to the existence of a secondary Pohlke’s projection closely related to the (always existing) projection given by Pohlke’s fundamental theorem of oblique axonometry.
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