The Bus Bunching Problem: Why Adding Buses Doesn't Work

2025-07-25
The Bus Bunching Problem: Why Adding Buses Doesn't Work

Imagine two buses on the same route, running on a schedule. One gets delayed by traffic. This delayed bus picks up passengers who would have taken the next bus, causing further delays. The next bus, meanwhile, makes better time due to fewer passengers. Eventually, the buses bunch together, sometimes with the second bus overtaking the first. Adding more buses isn't the solution; better strategies include managing stop times, skipping stops, encouraging passengers to take later buses, or, as Northern Arizona University did, abandoning fixed schedules altogether and manually controlling bus spacing for even distribution.

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Mysterious Light in Brussels Mausoleum: Coincidence or Design?

2025-06-11
Mysterious Light in Brussels Mausoleum: Coincidence or Design?

Every June 21st at midday, a shaft of light pierces the roof of a mausoleum in Brussels' Laeken Cemetery, creating a heart of light. It's unclear whether this was intentional. The tomb's occupants died in 1916 and 1919, with the mausoleum built in 1920. The designer is little known, and plans don't mention the light. The article also features a poem inscribed on the monument of Sir Lawrence Tanfield (d. 1625), expressing his wife's love and grief.

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Typographic Rivers: A Curious Case of Accidental Alignment

2025-05-19
Typographic Rivers: A Curious Case of Accidental Alignment

Have you ever noticed how sometimes the spaces between words in printed text coincidentally align to form vertical 'rivers' of whitespace? This phenomenon, most common in monospaced fonts with full justification, is generally avoided by typographers due to its distracting nature. The article cites a classic 12-line example discovered in 1988 and a collection from 1986, highlighting the intriguing randomness of this typographic quirk.

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Design

Visual Proof: a² – b² = (a + b)(a – b)

2024-12-15
Visual Proof: a² – b² = (a + b)(a – b)

Futility Closet's blog post presents a visual proof of the mathematical formula a² – b² = (a + b)(a – b), quoting Sophie Germain's insightful words: “It has been said that algebra is but written geometry and geometry is but diagrammatic algebra.” The post uses an easily understood diagram to demonstrate the formula, highlighting the elegance of mathematics and the strong relationship between algebra and geometry.

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