Shadows, Secrets & Surprises

On Halloween night, a witch wanted to know the height of the old tree outside her house. Climbing it was out of the question. Luckily, her cat was nearby.

The cat was 1 foot tall, and its shadow stretched 2 feet across the ground. The tree’s shadow stretched 30 feet.

The witch noticed that the moonlight hit the cat and the tree at the same angle. That meant their heights and shadows formed similar triangles.

1 / 2 = H / 30, so H = 15 feet

No ladder. No climbing. Just one cooperative cat, a long shadow, and a little geometry.

Same moonlight. Same ratio. Mystery solved.

Meet Sarah, a young flutist who enjoys exploring tone, technique, and tuning.

ODD Times: How do you adjust your sound and stay in tune with another player?

Sarah: I have to change my embouchure and my air speed. When you aren’t in tune with another person, you can hear clashing sound waves—it doesn’t sound great, lol!

Read the full interview →

Ever seen a photo where someone seems to hold the moon—or a tiny person stands on someone’s hand? That’s forced perspective. Objects appear smaller as they move farther away. By carefully choosing distance and viewing angle, photographers and filmmakers can make objects look much larger or smaller than they really are.

The result can fool your eyes, but the trick isn’t magic. It’s geometry.

On Halloween night, four jack-o’-lanterns tell some trick-or-treaters their heights and the lengths of their shadows. They’re standing on the same level ground under the same moonlight—but one is lying.

Which one is lying?

At midnight, 100 ghosts enter a hotel with 100 dark rooms.

The first ghost flips every light. The second flips every second light, the third every third—and so on. By morning, only ten rooms glow:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Why these? They’re all perfect squares. Most factors come in pairs, but a square has one factor—its square root—that pairs with itself, leaving its light flipped an odd number of times.

Even ghosts can’t escape mathematics.