. Consider a disk D of radius 1. We say a collection of shapes hides D...

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. Consider a disk D of radius 1. We say a collection of shapes hides D if we can place the shapes from that collection on top of the disk in such a way that cach point of the disk is under some part of at least one of the shapes. For example. D can be hidden by a single disk of radius greater-than-or-equal-to 1. However. D cannot be hidden by a single disk of smaller radius than 1. As another example. D can be hidden by 7 disks of radius 3/4 by placing one radius 3/4 disk at the center and the remaining radius 3/4 disks around the edge of D as follows: (a) Find the smallest radius r so that two disks of radius r hide D (and any disk of radius less than r cannot hide it). (b) What is the smallest radius r you can find such that four disks of radius r can hide D? (c) What is the smallest radius r that you can find such that five disks of radius r can hide D? You don't need to prove this radius is optimal; you only need to show that you found a solution with your radius r. With the radius you found, can you hide D in such a way that the centers of the disks are not vertices of a regular pentagon? . Consider a disk D of radius 1. We say a collection of shapes hides D if we can place the shapes from that collection on top of the disk in such a way that cach point of the disk is under some part of at least one of the shapes. For example. D can be hidden by a single disk of radius greater-than-or-equal-to 1. However. D cannot be hidden by a single disk of smaller radius than 1. As another example. D can be hidden by 7 disks of radius 3/4 by placing one radius 3/4 disk at the center and the remaining radius 3/4 disks around the edge of D as follows: (a) Find the smallest radius r so that two disks of radius r hide D (and any disk of radius less than r cannot hide it). (b) What is the smallest radius r you can find such that four disks of radius r can hide D? (c) What is the smallest radius r that you can find such that five disks of radius r can hide D? You don't need to prove this radius is optimal; you only need to show that you found a solution with your radius r. With the radius you found, can you hide D in such a way that the centers of the disks are not vertices of a regular pentagon?

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a Two disks of radius r to hide a disk D of radius 1 For any two disks to hide D their boundaries mu... View the full answer