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corrected to inclusive pronoun
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edit approved Jul 1, 2020 at 5:42
Greg Martin
edit approved Jul 1, 2020 at 5:42
Greg Martin
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Here is a straightforward escape route.

Go to the centre of the pool. Divide the pool into octants, and swim directly across the middle of the octant opposite your friend. In this picture your friend is somewhere along AE, where E is the midpoint of side AB. You swim directly to the point F, which is the point one quarter along side CD. By rotating/reflecting, this method works wherever your friend is.

enter image description here

Let'sLet us set the side length of the pool equal to 4. The distance you swim is $\sqrt{5}$, so your friend can run a distance of $3\sqrt{5}$, or about $6.7$. However, he needsthey need to run at least $7$ to go along ADF or along EBCF.

Here is a straightforward escape route.

Go to the centre of the pool. Divide the pool into octants, and swim directly across the middle of the octant opposite your friend. In this picture your friend is somewhere along AE, where E is the midpoint of side AB. You swim directly to the point F, which is the point one quarter along side CD. By rotating/reflecting, this method works wherever your friend is.

enter image description here

Let's set the side length of the pool equal to 4. The distance you swim is $\sqrt{5}$, so your friend can run a distance of $3\sqrt{5}$, or about $6.7$. However, he needs to run at least $7$ to go along ADF or along EBCF.

Here is a straightforward escape route.

Go to the centre of the pool. Divide the pool into octants, and swim directly across the middle of the octant opposite your friend. In this picture your friend is somewhere along AE, where E is the midpoint of side AB. You swim directly to the point F, which is the point one quarter along side CD. By rotating/reflecting, this method works wherever your friend is.

enter image description here

Let us set the side length of the pool equal to 4. The distance you swim is $\sqrt{5}$, so your friend can run a distance of $3\sqrt{5}$, or about $6.7$. However, they need to run at least $7$ to go along ADF or along EBCF.

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Jaap Scherphuis
Jaap Scherphuis
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Here is a straightforward escape route.

Go to the centre of the pool. Divide the pool into octants, and swim directly across the middle of the octant opposite your friend. In this picture your friend is somewhere along AE, where E is the midpoint of side AB. You swim directly to the point F, which is the point one quarter along side CD. By rotating/reflecting, this method works wherever your friend is.

enter image description here

Let's set the side length of the pool equal to 4. The distance you swim is $\sqrt{5}$, so your friend can run a distance of $3\sqrt{5}$, or about $6.7$. However, he needs to run at least $7$ to go along ADF or along EBCF.