S1

{
   "voice_prompt": "",
   "manuscript": {
       "title": {
           "text": "How to Build Pascal’s Triangle?",
           "audio": "How to build Pascal’s Triangle?"
       },
       "description": {
           "text": "You can build Pascal’s Triangle by starting with ones and adding together neighbouring numbers to fill in the rest.",
           "audio": "You can build Pascal’s Triangle by starting with ones and adding together neighbouring numbers to fill in the rest."
       },
       "scenes": [
           {
               "text": "Pascal’s Triangle is a pattern of numbers arranged in rows. You build it by starting with ones and adding together neighbouring numbers to fill in the rest.",
               "latex": "",
               "//": "Show Pascal's Triangle here (first 5 rows)"
           },
           {
               "text": "Each row starts and ends with one. To find the numbers in between, you simply add the two numbers directly above.",
               "latex": "",
               "//": "Show Pascal's Triangle growing with animation as numbers are added"
           },
           {
                "text": "For example, 1 plus 4 gives 5, and 4 plus 6 gives 10—this pattern continues throughout the triangle.",
               "latex": "",
               "//": "Show Pascal's Triangle growing with animation as numbers are added. Continue from row 5"
           },
           {              
               "text": "Each number in Pascal's Triangle also matches a combination, often called n choose k. The row number tells you n, and the position in the row tells you k. Notice that you start counting rows and positions at 0",
               "latex": "n \choose k"
           },
           {
               "text": "For example, row 3 gives you the combinations 3 choose 0, 3 choose 1, 3 choose 2, and 3 choose 3.",
               "latex": "\binom{3}{0}, \binom{3}{1}, \binom{3}{2}, \binom{3}{3}"
           },
           {
               "text": "If you calculate them, you get 1, 3, 3, and 1 — exactly what you see in row 3 of the triangle.",
               "latex": "1, 3, 3, 1",
               "//": "The rest of the scene should be the rest of the triangle, but the 1,3,3,1 row is highlighted."
           },
           {
               "text": "This makes Pascal's Triangle a quick way to find combination values without calculating each one from scratch.",
               "latex": "",
               "//": "Show Pascal's Triangle here (first 5 rows, written as n choose r). Bonus if it fades in from the 'normal' triangle"
           },
           {
               "text": "If you need a combination like 5 choose 2, just go to row 5, remember to start counting at 0, so row 5 is this one. And to find position 2, you need to count 0, 1 and 2. Here. That's the third number from the left.",
               "latex": "\binom{5}{2} = 10",
               "//": "Again, you can highlight/zoom in on the 5 choose 2 part and fade into normal triangle where 10 should now be in the same spot, highlighted."
           }
       ],
       "outro": {
           "text": "You can build Pascal’s Triangle by starting with ones and adding together neighbouring numbers to fill in the rest.",
           "audio": "You can build Pascal’s Triangle by starting with ones and adding together neighbouring numbers to fill in the rest"
       }
   }
}

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