Communicating a Proof

Saunders Mac Lane (1909 – 2005) was an American mathematician who became known for being one of the proponents of category theory. During an interview with The Mathematical Review in 1976, he reminisced about the time when he was learning about geometry in high school: I recall one occasion involving a theorem about a triangle: I knew […]

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Gleanings from the Past #75

Coining New Words Carl Sagan Physicists had to invent words and phrases for concepts far removed from everyday experience. It was their fashion to avoid pure neologisms and instead to evoke, even if feebly, some analogous commonplace. The alternative was to name discoveries and equations after one another. This they did also. But if you […]

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Another Match Equation Puzzle

Here’s another match equation puzzle. The illustration represents an incorrect Roman numerals equation (3 = 30). Move only two matches to make this equation valid. You cannot shift the position of the other matches. Solution (Click to Show) The solution involves Roman numerals and a multiplication sign. So, it can be read as: C = […]

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A Mathematical Proposal

There is a quaint story in Ripley’s Believe It or Not! 15th Series (1969) about a man who used mathematical terms to propose. Robert Greer, a mathematics teacher at the Mount School in York, England, made the following proposal to a girl named Anne in 1880: If R = 1/2 and A = 1/2, Then R + […]

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An Easier Match Puzzle

The above illustration depicts an invalid Roman numerals equation (the left side is 6 and the right side is 2) using seven matches. Find a way to correct this equation by only moving one match. You cannot shift the position of the other matches. Solution (Click to Show) As is equal to 1, the equation […]

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5 Interesting Exponent Patterns

1. Squares with Twin Halves 36,363,636,3642 = 1,322,314,049,613,223,140,496 The first 11 digits of the square are the same as the last 11 digits. This is the smallest possible solution for this pattern. Here’s another one: 63,636,363,6372 = 4,049,586,776,940,495,867,769. Furthermore, adding these two numbers results to: 36,363,636,364 + 63,636,636,637 = 100,000,000,001. 2. Consecutive Squares with a Cube Sum […]

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Fermat’s Last Theorem on the Subway Wall

When Pierre de Fermat conjectured his last theorem, of which what would be known as the Fermat’s Last Theorem, in 1637, he only wrote it on the margin of his copy of Arithmetica. He claimed that he knew the proof, but it was too large to fit in the narrow margin. H. H. Wu, mathematician […]

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Real World Probability: A “Birthday Problem” Anecdote

I heard the following story from my topology professor. A renowned statistician was teaching a course in fundamental probability theory to a group of undergraduates. As expected of an introductory course, he briefly tackled several main principles of probability to give the students a bird’s-eye view of the subject. One day, he talked about the […]

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Happy New Year 2019! (And Mathematical Facts About 2019)

Time by moments steals away, First the hour, and then the day; Small the daily loss appears, Yet it soon amounts to years. — John Newton, The Works of the Rev. John Newton, 1827 As the new year approaches, so is the second anniversary of Learn Fun Facts. But before that, let’s examine some numerical […]

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A Palindromic Magic Square for the Year 2019

The above 4 × 4 magic square only has the digits 2, 0. 1, and 9 (from the year 2019) and as a bonus, the four digits in its upper-left section form “2019”. It has a magic sum of 132. This means the sums of the magic square’s columns, rows, and diagonals are all equal […]

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