img

How many regions can you obtain from a single thick piece of cheese by making five straight cuts?(The cheese must stay in original position while you do all the cutting and each slice must correspond to a plane in 3D).Find a recurrence relation for \(P_n\),the maximum number of three dimensional regions that can be defined by \(n\) different planes.

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestWell I obtain 18 pieces cut 2 slices with a plane and other 2 with another plane and the last one with the last plane. But I am still thinking of a recurrence relation for \(P_n\)

Starting with

```

```

Somebody also think.

ARYΔ

Log in to reply

Hm. I feel like 4 cuts should give us more than 12 pieces. The second to third cut already gives us 4 additional pieces, and I would expect that the third to fourth cut would give us more.

Log in to reply