London Cabbies and Math: A Tale of Numbers in History
In the world of mathematics, there's a fascinating tale behind a number that has captivated mathematicians and puzzle enthusiasts alike - 1729. This year was chosen for its unique property as being "taxicab number," meaning it has no repeated digits when written in any base with up to four digits. But what does this have to do with London cabs?
To answer, we first need to look at three math puzzles that were recently posed by a clever puzzle maker.
Firstly, we're tasked with finding the smallest number that can be expressed as the sum of two different pairs of squares. After some digging, we find that 50 is such a number, being equal to both 1^2 + 7^2 and 5^2 + 5^2.
Next up, we have five strips of wood with lengths 1, 2, 7, 17, and 29 centimeters. The goal is to add another strip, with a maximum length of 29cm, such that no three strips can form a triangle. After exploring the possible combinations, we discover that there are two new lengths for the seventh strip: 3 and 4. It turns out these can be used to create a right-angled triangle with sides of length 3, 4, and 5.
Lastly, we're presented with four numbers - 'a', 'b', 'c', and 'd' - which may be whole numbers or fractions. We know that there are six ways to multiply two pairs of these numbers together. The products given are 2, 3, 4, 5, and 6. But what's the sixth product? By clever reasoning, we deduce it must be related to another pair of products - namely, 'ab' x 'cd', or 'ac' x 'bd', or 'ad' x 'bc'. After some algebraic manipulation, we arrive at a surprising answer: 2.4.
While these math puzzles might seem unrelated to London cabs at first glance, they are actually connected to a famous story from history - the one about two mathematicians, Hardy and Ramanujan, who took a taxi ride in London in 1928. According to legend, they got into a discussion about the number 1729. When asked if he knew of any larger number, Ramanujan replied with "No, but I can tell you one greater than that." This clever response remains an enduring testament to the power of math and its ability to bring people together - even across centuries and cultures.
While these puzzles may have no direct connection to cabbies, they do show us how numbers can weave their way through history, influencing our understanding of mathematics itself.
In the world of mathematics, there's a fascinating tale behind a number that has captivated mathematicians and puzzle enthusiasts alike - 1729. This year was chosen for its unique property as being "taxicab number," meaning it has no repeated digits when written in any base with up to four digits. But what does this have to do with London cabs?
To answer, we first need to look at three math puzzles that were recently posed by a clever puzzle maker.
Firstly, we're tasked with finding the smallest number that can be expressed as the sum of two different pairs of squares. After some digging, we find that 50 is such a number, being equal to both 1^2 + 7^2 and 5^2 + 5^2.
Next up, we have five strips of wood with lengths 1, 2, 7, 17, and 29 centimeters. The goal is to add another strip, with a maximum length of 29cm, such that no three strips can form a triangle. After exploring the possible combinations, we discover that there are two new lengths for the seventh strip: 3 and 4. It turns out these can be used to create a right-angled triangle with sides of length 3, 4, and 5.
Lastly, we're presented with four numbers - 'a', 'b', 'c', and 'd' - which may be whole numbers or fractions. We know that there are six ways to multiply two pairs of these numbers together. The products given are 2, 3, 4, 5, and 6. But what's the sixth product? By clever reasoning, we deduce it must be related to another pair of products - namely, 'ab' x 'cd', or 'ac' x 'bd', or 'ad' x 'bc'. After some algebraic manipulation, we arrive at a surprising answer: 2.4.
While these math puzzles might seem unrelated to London cabs at first glance, they are actually connected to a famous story from history - the one about two mathematicians, Hardy and Ramanujan, who took a taxi ride in London in 1928. According to legend, they got into a discussion about the number 1729. When asked if he knew of any larger number, Ramanujan replied with "No, but I can tell you one greater than that." This clever response remains an enduring testament to the power of math and its ability to bring people together - even across centuries and cultures.
While these puzzles may have no direct connection to cabbies, they do show us how numbers can weave their way through history, influencing our understanding of mathematics itself.
... but what's even more awesome is the story behind it - like, these two mathematicians getting into this convo about numbers and then taking a ride in a London cab 
. It just goes to show how important math is in our lives, even when we're not thinking about it... I wish they had puzzles about cabbies too 
, can you imagine? Like, what's the smallest fare that could be paid with a 20-pound note? 
! finding that sixth product was like solving a whole new world of algebra, and i love how it's all connected to those two mathematicians who actually took a taxi ride in london 
. but you know what really got me is how they tied everything back to 1729 - like, isn't that just the most beautiful example of math being everywhere at once? 
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. I love how math can bring people together like that. It's like, who cares if you're from different countries or cultures when you can geek out over numbers with someone? 
. Like, I need to see some calculations or something! 
. I mean, who knew that a number as simple as 1729 had such a rich history behind it? And the stories about Hardy and Ramanujan taking a taxi ride in London and discussing math... that’s just wild 
. Maybe they don’t realize it, but when they’re driving around, they’re using all sorts of mathematical calculations to get from one place to another 
. It’s funny how something as mundane as a taxi ride can be tied to something so fascinating as math 
, like who knew 1729 had such an awesome history behind it?! and btw, i'm still trying to wrap my head around the 50 = sum of squares thing - genius, right? 
. But let's be real, math problems are just a waste of time if you ask me 
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. And did you see those solutions? Like, who knew that 50 could be expressed as two different pairs of squares?! 
. It shows just how deeply ingrained math is in our culture and how it can bring people together even across time zones.
? It's almost as if we're reminded that there's more to life than just solving problems or meeting some arbitrary goal – it's about the journey itself and how it brings us closer to others and to ourselves.
and then they go n try to connect it to london cabbies but idk how they do dat cuz i mean, Hardy n Ramanujan were just chillin n talkin bout math n stuff not cabbies 