A child prodigy: Carl Friedrich Gauss
A child prodigy: Carl Friedrich Gauss
𝗜𝗻𝗱𝗲𝘅:
⏲ 0:00 Johann Carl Friedrich Gauss
⏲ 0:20 A child prodigy
⏲ 0:53 The problem
⏲ 1:45 The possible solutions
⏲ 3:24 Outro
📫𝐎𝐮𝐫 𝐅𝐁 𝐏𝐚𝐠𝐞:
/ scienceworld-106933907791981
🎬𝐈𝐦𝐚𝐠𝐞𝐬, 𝐚𝐧𝐢𝐦𝐚𝐭𝐢𝐨𝐧𝐬 𝐚𝐧𝐝 𝐯𝐢𝐝𝐞𝐨𝐬 𝐜𝐫𝐞𝐝𝐢𝐭𝐬:
Die Vermessung der Welt (Measuring the World) by Detlev Buck
Pexels
📚𝐃𝐚𝐯𝐢𝐝'𝐬 𝐁𝐨𝐨𝐤𝐬
📕 𝗪𝗲𝗶𝗿𝗱 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝗜𝗻𝗳𝗶𝗻𝗶𝘁𝘆 𝗮𝗻𝗱 𝗕𝗲𝘆𝗼𝗻𝗱
(https://www.amazon.com/Weird-Maths-Ag...)
📙 𝗪𝗲𝗶𝗿𝗱𝗲𝗿 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝘁𝗵𝗲 𝗣𝗼𝘀𝘀𝗶𝗯𝗹𝗲
(https://www.amazon.com/Weirder-Maths-...)
📗 𝗪𝗲𝗶𝗿𝗱𝗲𝘀𝘁 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗙𝗿𝗼𝗻𝘁𝗶𝗲𝗿𝘀 𝗼𝗳 𝗥𝗲𝗮𝘀𝗼𝗻
(https://www.amazon.com/Weirdest-Maths...)
** The kindle versions are available
*** For more details : http://weirdmaths.com/
📄𝗧𝗿𝗮𝗻𝘀𝗰𝗿𝗶𝗽𝘁𝗶𝗼𝗻:
Johann Carl Friedrich Gauss was a German mathematician and physicist, who made significant contributions to many fields in mathematics and science. Because of his work, his name has been given to many rules, methods, and inventions.
After his death in 1855, Gauss’s friend, the geologist Wolfgang Sartorius von Waltershausen, wrote his biography. Waltershausen pointed out that even as a little boy, Gauss showed extraordinary mental powers. He learned to read by asking members of his family the sound of letters and learned to count before he could talk. When he was only 3 years old, he corrected a mistake in his father's business accounts.
According to Waltershausen, Gauss’ schoolteacher J. G. Büttner one day gave an arithmetic problem to the class. The task was to add all the numbers from 1 to 100 in one hour. Most of the pupils naturally began to add the numbers one by one on their slates, but Gauss wrote nothing. He just thought for a minute, wrote the answer to the question on his slate, stood up, and threw his slate on the table with the words "There it lies", while everyone else continued busily adding. After the hour was up, Büttner checked the pupils’ slates. He saw that Gauss’ result was correct whereas many of the others were wrong. How could a primary school child solve the problem so quickly?
Some researchers believe that Gauss folded the series like this (2). If we sum the numbers vertically, we end up with the same result, 101. Since there are 50 sums, the result is 101 times 50, or 5,050.
Other researchers think that Gauss wrote another series under the first in reverse order and added the numbers vertically as before, giving the result 101. Since there are 100 sums, that makes 100 times 101, but because there are two series Gauss divided the sum by 2 and found the result: again 5,050.
Another possible approach is averaging. If we consider the first and the last number, their average is (1 + 100)/2, which is 50.5. We get 100 times 50.5, which again leads us to the answer: 5,050
We’re not sure which method Gauss actually used. But the story illustrates a general point: problems in maths or science can be much easier to solve or understand if we manage to find the right approach.
#carl #gauss #series