30th Irish Mathematical Olympiad – 2017 Roll of Honour 1 Cillian Doherty

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Ireland’s Participation in the 57th International Mathematical Olympiad Bernd Kreussler August 16, 2016 From 6th until 16th July 2016, the 57th International Mathematical Olympiad took place in Hong Kong. This was the

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The Acorn Spring 2014 South Carolina Tree Climbing Academy May 29, 2014 Irmo, SC

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• Biology
• Natural environment
• Environmental design
• Trees
• Forest management
• Biophilia hypothesis
• Urban forestry
• Tree
• Pest
• Permaculture
• Arboriculture
• Urban forest

The Acorn Spring 2015 South Carolina Tree Climbing Academy May 21, 2015 Irmo, SC

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• Biophilia hypothesis
• Urban forestry
• Arborist
• Tree
• Oak
• Tree City USA
• Trees Atlanta

8. Lemoine Point and Circles. Theorem 1 In a triangle ABC the distances from the Lemoine point L to the sides are in the ratio αa, αb, αc,

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Chapter 1. The Medial Triangle 2 The triangle formed by joining the midpoints of the sides of a given triangle is called the medial triangle. Let A1 B1 C1 be the medial triangle of the triangle ABC in Figure 1. The sid

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2. Equilateral Triangles Recall the well-known theorem of van Schooten. Theorem 1 If ABC is an equilateral triangle and M is a

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5. Orthic Triangle. Let ABC be a triangle with altitudes AA2 , BB2 and CC2 . The altitudes are concurrent and meet at the orthocentre H (Figure 1). The triangle formed by the feet of the altitudes, A2 B2 C2 is the orthi

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7. Lemoine Point. Two lines AS and AT through the vertex A of an angle are said to be isogonal if they are equally inclined to b or equivalently, to the bisector of A b (Figure the arms of A,

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Ireland’s Participation in the 56th International Mathematical Olympiad Mark Flanagan December 9, 2015 This document contains a report on Ireland’s participation in the 56th International Mathematical Olympiad (IMO).

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