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[Chinese] 2024/shorts/cube-shadow-puzzle
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ZstringX authored Feb 5, 2024
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]
},
{
"translatedText": "假设您在三维空间中随机定位一个立方体,然后查看其阴影区域",
"translatedText": "假设你在三维空间中以随机朝向放置一个立方体,然后观察其阴影区域",
"input": "Suppose you randomly orient a cube in three-dimensional space, and you look at the area of its shadow.",
"time_range": [
1.66,
7.56
]
},
{
"translatedText": "该区域的预期价值是多少",
"translatedText": "该区域的预期面积是多少",
"input": "What's the expected value for that area?",
"time_range": [
8.04,
10.04
]
},
{
"translatedText": "或者换句话说,如果你一遍又一遍地重复这个过程,随机扔掉那个立方体并统计你发现的面积,那么当你越来越多地这样做时,所有这些测量面积的经验测量平均值会接近什么",
"translatedText": "或者换句话说,如果你一遍又一遍地重复这个过程,随机扔那个立方体并统计你得到的面积,那么当你这样做越来越多次时,所有这些测得面积的经验测量平均值会接近什么",
"input": "Or phrased another way, if you repeat this process over and over, randomly tossing that cube and tallying up the areas that you find, what would the empirically measured mean of all those measured areas approach as you do this more and more?",
"time_range": [
10.7,
22.64
]
},
{
"translatedText": "严格来说,在引用阴影时,这取决于光源在哪里,但在这里我们正在做典型的数学家的事情,将光源视为无限远,所以阴影只是一个平面投影,比如说,到 xy 平面上。",
"translatedText": "严格来说,在提到阴影时,这将取决于光源在哪里,但在这里我们以典型的数学家的思维方式,将光源视为无限远,所以阴影只是一个平面投影,比如说,到 xy 平面上。",
"input": "Strictly speaking, in referencing the shadow, that would depend on where the light source is, but here we're doing the typical mathematician thing of thinking of the light source as being infinitely far away, so the shadow is just a flat projection, say, onto the xy-plane.",
"time_range": [
23.24,
35.66
]
},
{
"translatedText": "这绝对是一个难题,我实际上很好奇你会在评论中如何解决它",
"translatedText": "这绝对是一个难题,我实际上很好奇在评论中你会如何解决它",
"input": "It is definitely a hard problem, and I'm curious actually to hear how you would approach it in the comments.",
"time_range": [
36.06,
Expand All @@ -56,19 +56,19 @@
]
},
{
"translatedText": "事实上,这是一个关于两种不同的解决问题风格的传奇,以及为什么数学的普及往往会对它们所代表的风格产生偏见。",
"translatedText": "事实上,这是一个关于两种不同的解决问题的风格的传奇故事,以及为什么数学的普及往往会对它们所代表的风格产生偏见。",
"input": "Really, it's a saga about two distinct problem-solving styles, and why popularizations of math tend to have a bias in what kinds of styles they represent.",
"time_range": [
44.82,
52.4
]
},
{
"translatedText": "事实证明,影子谜题是这个故事的一个非常完美的背景",
"translatedText": "事实证明,影子谜题是这个故事的一个非常完美的场景",
"input": "The shadow puzzle just turns out to be a very perfect setting for that story.",
"time_range": [
52.76,
55.98
]
}
]
]

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