Numerical Estimation.

Presentation on theme: "Numerical Estimation."— Presentation transcript:

1 Numerical Estimation

2 “” means “approximately equal to”
Recall Your Memory I 1 2 1 4 1 5 exact value = 0.5 = 0.25 = 0.2 1 3 approximate value 1 6  0.33  0.67 “” means “approximately equal to”

3 Recall Your Memory II Round off correct to the nearest hundred. Round off correct to the nearest hundred. 8120 8170 8100 8200

4 How many are there in our school?
Case I How many are there in our school?

5 Case II What is the travelling time from to by ?

6 Case III has and would like to buy the following products in a supermarket: $101.5 $99.1 $80.7 Does have enough money?

7 Case IV can carry 49 passengers. Now, there are and 10 to go for a picnic. How many do they need?

8 Is it possible? Case V would like to order 9 over the phone.
Each costs $52.5. shows $ Is it possible?

9 Why do we need estimation?
For easier calculation When the original number is unknown The value may vary a bit in different situation Limitations in measurement Checking whether the result is reasonable

10 A history of  (希臘) 圓周率的發展 年代 求證者 內容 古代 中國周髀算經 西方聖經 周一徑三 圓周率 ＝ 3 元前三世紀
 圓周率 ＝ 3 元前三世紀 阿基米德 (希臘) 1.  圓面積等於分別以半圓周和徑為邊長的    矩形的面積 2.   圓面積與以直徑為長的正方形面積     之比為11:14 3.  圓的周長與直徑之比小於3 1/7 ,大於     310/71

11 中國 荷蘭 三世紀 劉徽 用割圓術得圓周率＝3.1416稱為'徽率' 五世紀 祖沖之 1. 3.1415926＜圓周率＜3.1415927
2. 約率 ＝ 22/7 3. 密率 ＝ 355/113 1596年 魯道爾夫 荷蘭 正確計萛得p的35 位數字

12 法國 英國 1579年 韋達 '韋達公式'以級數無限項乘積表示p 1600年 威廉.奧托蘭特 用p/σ表示圓周率 π是希臘文圓周的第一個字母
σ是希臘文直徑的第一個字母 1655年 渥里斯 開創利用無窮級數求p的先例