【ChatGPT 實戰13】數學計算、數學問題

如果把 ChatGPT 當成計算機或數學老師,這又行不行呢?以下是小編實測的例子。


【例】詢問數學方程式。

問:What’s the formula of calculating a sphere’s volume?

ChatGPT:

The formula for the volume of a sphere is:

V = (4/3)πr³

Where V is the volume of the sphere, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.


【例】釐清數學概念。

問:Is it possible to have a limit at infinity?

ChatGPT:

Yes, it is possible to have a limit as a variable approaches infinity. In mathematics, we often use limits to describe the behavior of functions as their inputs approach certain values, such as infinity.

For example, the limit of the function f(x) = 1/x as x approaches infinity is 0. This means that as x gets larger and larger, the value of f(x) gets closer and closer to 0, but it never actually reaches 0.

Limits at infinity are an important concept in calculus, and they are used to study the behavior of functions on a large scale.


【例】詢問經濟上的數學問題。

ChatGPT:

If Sam’s monthly income is 20,000 and his monthly expenses are 15,000, he has a monthly surplus of 20,000 – 15,000 = 5,000.

If Sam wants to buy a house costing $5,000,000, he will need to make a down payment or first installment. If the first installment is $1,000,000, he will need to save up for it.

To determine how long it will take Sam to save up for the first installment, we can use the formula:

time = amount needed to save / monthly surplus

Plugging in the values, we get:

time = $1,000,000 / $5,000 = 200 months

Therefore, Sam will need to save for around 200 months, or a little over 16 years, to accumulate the $1,000,000 he needs for the first installment.


【例】推理問題。

1+4=5

2+5=12

3+6=21

8+11=?

在網路上的答法有 2 個,一個答案是 40,另一個答案則是 96。

不過,ChatGPT 似乎不太能理解,結果給出了 209 的答案。


【例】數學計算。

問:There are 49 balls in a bag, 17 are red balls, 16 are blue balls, 16 are green balls, what is the probability that the 6 balls picked are all red?

ChatGPT: No problem!

To find the probability of picking 6 all-red balls out of 49, we can use the formula for combinations. The number of ways to select 6 balls out of the 17 red balls is given by:

C(17,6) = (17!)/(6!(17-6)!) = 12376

Therefore, there are 12,376 ways of selecting 6 all-red balls.

The total number of ways to select 6 balls out of 49 is given by:

C(49,6) = (49!)/(6!(49-6)!) = 13983816

Therefore, there are 13,983,816 ways of selecting any 6 balls out of the bag.

The probability of selecting 6 all-red balls is then:

P(all-red) = number of ways of selecting 6 all-red balls / total number of ways of selecting 6 balls

= 12376 / 13983816

≈ 0.000885 or about 0.0885%

Therefore, the probability of picking all 6 balls as red from the bag is approximately 0.000885 or 0.0885%. This is a very small probability, indicating that it is unlikely to pick all 6 balls as red from the bag.


後語:除了人設計的推理問題外,似乎對於中學程度的數學問題,ChatGPT 也能應付得來。

閱讀更多實戰教學>>>【文章索引1-40】ChatGPT 實例教學全示範

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