## Forum Geometricorum

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• The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2013volume13/FG201308ndex.html The editors Forum
Message 1 of 476 , Apr 11, 2013
The following paper has been published in Forum Geometricorum. It can be viewed at

http://forumgeom.fau.edu/FG2013volume13/FG201308ndex.html
The editors
Forum Geometricorum
GrĂ©goire Nicollier, Convolution filters for triangles,
Forum Geometricorum, 13 (2013) 61--85.

Abstract. The construction of a new triangle by erecting similar ears on the sides of a given triangle (as in Napoleon's theorem) can be considered as the convolution of the initial triangle with another triangle. We use the discrete Fourier transformation and a shape function to give a complete and explicit description of such convolution filters and their iterates. Our method leads to many old and new results in a very direct way.

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• The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html The editors Forum
Message 476 of 476 , Apr 16, 2013
The following paper has been published in Forum Geometricorum. It can be viewed at

http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html

The editors
Forum Geometricorum

Paul Yiu, On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line,
Forum Geometricorum, 13 (2013) 87--102.

Abstract. Let L be a line intersecting the sidelines of triangle ABC at X, Y, Z respectively. The lines joining these intercepts to the centroid give rise to six more intercepts on the sidelines which lie on a conic Q(L,G). We show that this conic (i) degenerates in a pair of lines if L is tangent to the Steiner inellipse, (ii) is a parabola if L is tangent to the ellipse containing the trisection points of the sides, (iii) is a rectangular hyperbola if L is tangent to a circle C_G with center G. We give a ruler and compass construction of the circle C_G. Finally, we also construct the two lines each with the property that the conic Q(L,G) is a circle.

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