Have you ever tried to move a large piece of furniture through a narrow hallway and found yourself stuck? Here we'll explore the classic problem: what is the longest ladder/piece of furniture that can make it around the corner in this hallway? [b]Controls[/b] [list] [*]Use the sliders for [b][i]a[/i][/b] and [b][i]b[/i][/b] to adjust the widths of the hallways. [*]Drag point [b][i]C[/i][/b] to move the ladder through and see the longest possible ladder for that position. [/list] [i]Note: This is my first posting to GeoGebraTube.[/i]
[list=1] [*]Set a = 2 and b = 2. Slide point C to minimize the length of the ladder. What do you notice about the shape? [*]Set b = 4. Now slide C to minimize the length of the ladder. What has changed? [*]Try to generalize the relationship between a & b and the location of C. [*]Challenge: How could you extend this simulation to three dimensions? [/list]