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<blockquote data-quote="Chris_Nightwing" data-source="post: 5961917" data-attributes="member: 882">Ok, let's work this out geometrically without a grid. If creatures are circles, let's say a human is a circle with diameter 1, an ogre with diameter 2. Using the reach rules from grid combat, the distance between the edge of a human circle and the edge of a circle it is attacking must be 0 - they must touch. Ogres have 10' reach, so they can have a 5' gap between the edge of their circle and an enemy circle - which in this system is length 1. So we have a circle diameter 2, a gap of 1 and a circle of diameter 1 - the distance D between the centre of the ogre and the centre of the human is 1 + 1 + 1/2 = 2.5. Let's cram another ogre in right next to the first, so that its centre is also 2.5 away from the human and it can attack the human. The distance between the centres of the two ogres is 1 + 1 = 2. This sets up an isoceles triangle with side lengths 2.5, 2.5 and 2. Using some trigonometry, the angle between the lines connecting the human centre with the two ogre centres is 47.2 degrees - and thus, in a complete circle only 7 ogres could attack the human - not 8, definitely not 9.</blockquote>

[QUOTE="Chris_Nightwing, post: 5961917, member: 882"] Ok, let's work this out geometrically without a grid. If creatures are circles, let's say a human is a circle with diameter 1, an ogre with diameter 2. Using the reach rules from grid combat, the distance between the edge of a human circle and the edge of a circle it is attacking must be 0 - they must touch. Ogres have 10' reach, so they can have a 5' gap between the edge of their circle and an enemy circle - which in this system is length 1. So we have a circle diameter 2, a gap of 1 and a circle of diameter 1 - the distance D between the centre of the ogre and the centre of the human is 1 + 1 + 1/2 = 2.5. Let's cram another ogre in right next to the first, so that its centre is also 2.5 away from the human and it can attack the human. The distance between the centres of the two ogres is 1 + 1 = 2. This sets up an isoceles triangle with side lengths 2.5, 2.5 and 2. Using some trigonometry, the angle between the lines connecting the human centre with the two ogre centres is 47.2 degrees - and thus, in a complete circle only [b]7[/b] ogres could attack the human - not 8, definitely not 9. [/QUOTE]

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