Today’s date, written in the familiar American shorthand, is 10/24/26. At first glance, there is nothing particularly remarkable about it. But square those three numbers, and a familiar relationship emerges:
10^2 + 24^2 = 26^2The arithmetic works out neatly. One hundred plus 576 equals 676. Today’s date forms a Pythagorean triple, a set of three positive integers that can serve as the side lengths of a right triangle.
That gives October 24 a small mathematical distinction. The calendar has handed us a geometry problem with the answer already attached.
A Familiar Triangle in Disguise
Most of us first encountered the Pythagorean theorem in school. For a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side, called the hypotenuse:
a^2 + b^2 = c^2The theorem applies whether the side lengths are whole numbers, fractions, or irrational numbers. Pythagorean triples are the special cases in which all three lengths are positive integers. The most familiar example is probably 3, 4, 5. Another is 5, 12, 13.
That second triple explains today’s date. Divide each of our three numbers by two:
(10,24,26) = 2(5,12,13)Our calendar triangle is a scaled version of the 5-12-13 triangle. Every side has doubled, while the angles remain unchanged. The two triangles are similar, although the larger one has four times the area.
Mathematicians call 5, 12, 13 a primitive Pythagorean triple because the three numbers have no common divisor greater than one. The triple 10, 24, 26 is not primitive. It belongs to the same family, enlarged by a common multiplier.
Where the Numbers Come From
Pythagorean triples can seem like numerical accidents when encountered one at a time. Yet there is a systematic way to generate them. For positive integers , the following expressions produce a Pythagorean triple:
a=m^2-n^2,\qquad b=2mn,\qquad c=m^2+n^2Choose 3 for and 2 for . The first expression gives 9 minus 4, or 5. The second gives 12. The third gives 9 plus 4, or 13. Double those results, and we arrive at 10, 24, 26.
The formula works because of an algebraic identity:
(m^2-n^2)^2+(2mn)^2=(m^2+n^2)^2Expanding the left side reveals why. The negative middle term from the first square is offset by part of the second term, leaving exactly the expansion of the expression on the right. What initially looks like a lucky match turns out to follow from a general relationship.
There are infinitely many Pythagorean triples. Dates, however, impose much tighter restrictions. A month cannot exceed 12, and a day cannot exceed 31. Only a small portion of that infinite mathematical landscape can fit onto a calendar.
The Calendar Supplies the Coincidence
There is a qualification here. The pattern depends on how we write the date. We use 26 for the year rather than 2026. In a day-first format, the date becomes 24/10/26, which preserves the relationship because exchanging the two shorter sides changes nothing.
Writing the full year removes this particular pattern:
10^2+24^2\ne2026^2That dependence on notation is part of the appeal. The calendar does not possess some hidden geometric force. We have chosen a way of recording dates that occasionally places meaningful numerical relationships in front of us.
Recognizing that distinction lets us enjoy the coincidence without asking it to explain more than it does. There is no reason to expect today’s events to follow a special course because its abbreviated date describes a right triangle. There is, however, a good reason to pause over the arithmetic.
A Small Invitation to Notice
I like these moments because they make familiar ideas briefly unfamiliar again. A theorem remembered from school appears in the corner of a computer screen. Three ordinary numbers become the sides of a triangle. A date becomes an invitation to investigate.
Following that invitation takes us from arithmetic to geometry, then to scaling, algebra, and the distinction between a pattern and the notation that reveals it. That is a respectable amount of mathematics to find in a date.
October 24, 2026, will pass like any other day. For a moment, though, we can picture it as a triangle: ten units across, twenty-four units up, and twenty-six units along the diagonal. The numbers fit, and noticing why is a pleasure.
Postscript
Check this out. We will have to wait a while for the next one.
| Occasion | Date | Pythagorean relationship |
| Previous | July 24, 2025 | 7² + 24² = 25² |
| Today | October 24, 2026 | 10² + 24² = 26² |
| Next | March 4, 2105 | 3² + 4² = 5² |
So today is the last such date this century. The next is more than 78 years away, followed shortly by April 3, 2105, which reverses the two shorter sides. Not bad, in fact, that is pretty cool.
