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人教版高中數學選修3排列與排列數教學設計
4.有8種不同的菜種,任選4種種在不同土質的4塊地里,有 種不同的種法. 解析:將4塊不同土質的地看作4個不同的位置,從8種不同的菜種中任選4種種在4塊不同土質的地里,則本題即為從8個不同元素中任選4個元素的排列問題,所以不同的種法共有A_8^4 =8×7×6×5=1 680(種).答案:1 6805.用1、2、3、4、5、6、7這7個數字組成沒有重復數字的四位數.(1)這些四位數中偶數有多少個?能被5整除的有多少個?(2)這些四位數中大于6 500的有多少個?解:(1)偶數的個位數只能是2、4、6,有A_3^1種排法,其他位上有A_6^3種排法,由分步乘法計數原理,知共有四位偶數A_3^1·A_6^3=360(個);能被5整除的數個位必須是5,故有A_6^3=120(個).(2)最高位上是7時大于6 500,有A_6^3種,最高位上是6時,百位上只能是7或5,故有2×A_5^2種.由分類加法計數原理知,這些四位數中大于6 500的共有A_6^3+2×A_5^2=160(個).
人教版高中數學選修3超幾何分布教學設計
探究新知問題1：已知100件產品中有8件次品，現從中采用有放回方式隨機抽取4件．設抽取的4件產品中次品數為X，求隨機變量X的分布列.（1）：采用有放回抽樣，隨機變量X服從二項分布嗎？采用有放回抽樣，則每次抽到次品的概率為0.08，且各次抽樣的結果相互獨立,此時X服從二項分布,即X～B(4，0.08).（2）：如果采用不放回抽樣，抽取的4件產品中次品數X服從二項分布嗎？若不服從，那么X的分布列是什么？不服從，根據古典概型求X的分布列.解：從100件產品中任取4件有 C_100^4 種不同的取法，從100件產品中任取4件，次品數X可能取0,1,2,3,4.恰有k件次品的取法有C_8^k C_92^(4-k)種.一般地，假設一批產品共有N件，其中有M件次品．從N件產品中隨機抽取n件(不放回），用X表示抽取的n件產品中的次品數，則X的分布列為P(X＝k）＝CkM Cn－kN－M CnN ，k＝m，m＋1，m＋2，…，r.其中n，N，M∈N*，M≤N，n≤N，m＝max{0，n－N＋M}，r＝min{n，M}，則稱隨機變量X服從超幾何分布．
人教版高中數學選修3條件概率教學設計
(2)方法一:第一次取到一件不合格品,還剩下99件產品,其中有4件不合格品,95件合格品,于是第二次又取到不合格品的概率為4/99,由于這是一個條件概率,所以P(B|A)=4/99.方法二:根據條件概率的定義,先求出事件A,B同時發(fā)生的概率P(AB)=(C_5^2)/(C_100^2 )=1/495,所以P(B|A)=(P"(" AB")" )/(P"(" A")" )=(1/495)/(5/100)=4/99.6.在某次考試中,要從20道題中隨機地抽出6道題,若考生至少答對其中的4道題即可通過;若至少答對其中5道題就獲得優(yōu)秀.已知某考生能答對其中10道題,并且知道他在這次考試中已經通過,求他獲得優(yōu)秀成績的概率.解:設事件A為“該考生6道題全答對”,事件B為“該考生答對了其中5道題而另一道答錯”,事件C為“該考生答對了其中4道題而另2道題答錯”,事件D為“該考生在這次考試中通過”,事件E為“該考生在這次考試中獲得優(yōu)秀”,則A,B,C兩兩互斥,且D=A∪B∪C,E=A∪B,由古典概型的概率公式及加法公式可知P(D)=P(A∪B∪C)=P(A)+P(B)+P(C)=(C_10^6)/(C_20^6 )+(C_10^5 C_10^1)/(C_20^6 )+(C_10^4 C_10^2)/(C_20^6 )=(12" " 180)/(C_20^6 ),P(E|D)=P(A∪B|D)=P(A|D)+P(B|D)=(P"(" A")" )/(P"(" D")" )+(P"(" B")" )/(P"(" D")" )=(210/(C_20^6 ))/((12" " 180)/(C_20^6 ))+((2" " 520)/(C_20^6 ))/((12" " 180)/(C_20^6 ))=13/58,即所求概率為13/58.
人教版高中數學選修3正態(tài)分布教學設計
3.某縣農民月均收入服從N(500,202)的正態(tài)分布,則此縣農民月均收入在500元到520元間人數的百分比約為 . 解析:因為月收入服從正態(tài)分布N(500,202),所以μ=500,σ=20,μ-σ=480,μ+σ=520.所以月均收入在[480,520]范圍內的概率為0.683.由圖像的對稱性可知,此縣農民月均收入在500到520元間人數的百分比約為34.15%.答案:34.15%4.某種零件的尺寸ξ(單位:cm)服從正態(tài)分布N(3,12),則不屬于區(qū)間[1,5]這個尺寸范圍的零件數約占總數的 . 解析:零件尺寸屬于區(qū)間[μ-2σ,μ+2σ],即零件尺寸在[1,5]內取值的概率約為95.4%,故零件尺寸不屬于區(qū)間[1,5]內的概率為1-95.4%=4.6%.答案:4.6%5. 設在一次數學考試中,某班學生的分數X~N(110,202),且知試卷滿分150分,這個班的學生共54人,求這個班在這次數學考試中及格(即90分及90分以上)的人數和130分以上的人數.解:μ=110,σ=20,P(X≥90)=P(X-110≥-20)=P(X-μ≥-σ),∵P(X-μσ)≈2P(X-μ130)=P(X-110>20)=P(X-μ>σ),∴P(X-μσ)≈0.683+2P(X-μ>σ)=1,∴P(X-μ>σ)=0.158 5,即P(X>130)=0.158 5.∴54×0.158 5≈9(人),即130分以上的人數約為9人.
新人教版高中英語選修1Unit 3 Fascinating Parks教案
2. Explore the significance of the establishment of Sarek National Park.Q1: Which event is the most important one in the park’s history?Ss: The establishment of Sarek national park in 1909 is the most important one.Q2: Is it worth making a place like Sarek a national park? Give your reasons.Ss: Yes. In this way, the place can be kept in its natural state and natural beauties and other rare and valuable resources can be preserved instead of being destroyed by endless exploitation driven by profits.Q3: How does the writer organize his introduction to the history of Sarek?Ss: The writer organizes his introduction in the sequence of time, using time indicators such as “used to”, “around 9,000 years ago”, “soon after”, “following the reindeer”, and “in 1909”.Q4: What is the feature of the language used to introduce the history of the park?Ss: The introduction to the park is to provide facts, using time indicators to organize the events. Sentences starts with “third person” and passive voice is used more often, feeling objective.【設計意圖】學生尋找和梳理公園歷史上的重要事件，體會人與自然的和諧關系，評鑒介紹性語言的特點。【核心素養(yǎng)提升點】發(fā)展自主提取、梳理文本信息能力，訓練邏輯思維和高階思維。Activity 3: Highlighting the secret of the text
新人教版高中英語選修2Unit 3 Learning about Language教學設計
1. We'll need ten months at least to have the restaurant decorated.2.Some traditional Chinese dishes from before the Ming Dynasty are still popular today.3.My grandpa's breakfast mainly includes whole grain biscuits and a glass of milk.4.People in this area would eat nearly a kilo of cheese per week.5. We enjoyed a special dinner in a fancy restaurant where the waiters all wore attractive suits.6. He prefers this brand of coffee which, as he said, has an unusually good flavor.Key:1. at a minimum 2. prior to3. consist of4. consume5. elegant6. exceptionalStep 5：Familiarize yourself with some food idioms by matching the meaning on the right with the colored words on the left.1.Public concern for the health of farm animals has mushroomed in the UK2.Anderson may be young but he's certainly rolling to doing dough!3.George is a popular lecturer. He often peppers his speech with jokes.4.As the person to bring home the bacon, he needs to find a stable job.5 He is often regarded as a ham actor for his over emphasized facial expressions. The media reported that these companies had treated pollution as a hot potato. 6.The media reported that these companies had treated pollution as a hot potato.7.Don't worry about the test tomorrow. It's going to be a piece of cake!8. It's best to fold the swimming ring when it is as flat as a pancake.A. completely flatB. something that is very easy to do C.an issue that is hard to deal withD.to include large numbers of somethingE.to earn on e's living to support a familyF. wealthyG.to rapidly increase in numberH. an actor who performs badly, especially by over emphasizing emotions
新人教版高中英語選修2Unit 3 Reading for writing教學設計
The theme of this part is to write an article about healthy diet. Through reading and writing activities, students can accumulate knowledge about healthy diet, deepen their understanding of the theme of healthy diet, and reflect on their own eating habits. This text describes the basic principles of healthy diet. The author uses data analysis, definition, comparison, examples and other methods. It also provides a demonstration of the use of conjunctions, which provides important information reference for students to complete the next collaborative task, writing skills, vivid language materials and expressions.1. Teach Ss to learn and skillfully use the new words learned from the text.2. Develop students’ ability to understand, extract and summarize information.3. Guide students to understand the theme of healthy diet and reflect on their own eating habits.4. To guide students to analyze and understand the reading discourse from the aspects of theme content, writing structure, language expression, etc., 5. Enable Ss to write in combination with relevant topics and opinions, and to talk about their eating habits.1. Guide students to analyze and understand the reading discourse from the aspects of theme content, writing structure, language expression, etc.2. Enable them to write in combination with relevant topics and opinions, and to talk about their eating habits.3. Guide the students to use the cohesive words correctly, strengthen the textual cohesion, and make the expression fluent and the thinking clear.Step1: Warming upbrainstorm some healthy eating habits.1.Eat slowly.2.Don’t eat too much fat or sugar.3.Eat healthy food.4.Have a balanced diet.Step2: Read the passage and then sum up the main idea of each paragraph.
新人教版高中英語選修2Unit 3 Using langauge-Listening教學設計
1． How is Hunan cuisine somewhat different from Sichuan cuisine?The heat in Sichuan cuisine comes from chilies and Sichuan peppercorns. Human cuisine is often hotter and the heat comes from just chilies.2.What are the reasons why Hunan people like spicy food?Because they are a bold people. But many Chinese people think that hot food helps them overcome the effects of rainy or wet weather.3.Why do so many people love steamed fish head covered with chilies?People love it because the meat is quite tender and there are very few small bones.4.Why does Tingting recommend bridge tofu instead of dry pot duck with golden buns?Because bridge tofu has a lighter taste.5 .Why is red braised pork the most famous dish?Because Chairman Mao was from Hunan, and this was his favorite food.Step 5: Instruct students to make a short presentation to the class about your choice. Use the example and useful phrases below to help them.? In groups of three, discuss what types of restaurant you would like to take a foreign visitor to, and why. Then take turns role-playing taking your foreign guest to the restaurant you have chosen. One of you should act as the foreign guest, one as the Chinese host, and one as the waiter or waitress. You may start like this:? EXAMPLE? A: I really love spicy food, so what dish would you recommend?? B: I suggest Mapo tofu.? A: Really ? what's that?
新人教版高中英語選修3Unit 1 Art教案
[2] An important breakthrough…was… [3] Another innovation was … [4] the emphasis increasingly shifted from…to… [5] New ideas and values gradually replaced… [6] While his paintings still had religious themes… … T: All these expressions serve to show how Western painting has developed. Some of them share similar structure but with varied use of words, which makes the text vivid and more readable. 【設計意圖】主題類語言整理有助于學生類化語言應用，提高語言輸出的豐富性。處理完文本內容信息后，進入語篇信息處理，進行主題相關的詞塊歸類。引導學生快速閱讀，尋找表達相同主題(發(fā)展或者藝術)的詞和短語，再根據詞性、用法和結構進行歸類，儲備主題相關詞匯，豐富語言儲備，提升語言素養(yǎng)。 Assignment: Go online to gather more information about Chinese painting and write a short history of it. 【設計意圖】結合所學，遷移運用，根據實際語境，進行模仿性運用。在此過程中，學生嘗試借鑒已學的語言、內容、語篇結構和寫作手法來建構新文本，實現語篇輸出，同時關注中西藝術文化的差別，加深對優(yōu)秀文化的認同，培養(yǎng)文化意識。
新人教版高中英語選修3Unit 2 Healthy Lifestyle教案
Activity 4: Figuring out the structure and the writing purpose 本活動為實現課時目標2。 1.Read Paragraph 6 and think about its main idea and the writer’s writing purpose. Q1: If you were the author, how would you end your article? “For young people, there is plenty of time to change bad habits. However, there is no “magic pill” or delete button that will help you; you have to think about your bad habits and decide on some changes. You have the power to build a happy and healthy life full of good habits!” Q2: What is Paragraph 6 mainly about? (Possible answer: to appeal to young people including teenagers to change bad habits and live a happy and healthy life.) 2.Think about the writer’s writing purpose and share opinions. Q1: What is the writing purpose? Work in pairs and figure it out. (Possible answer: On the one hand, the passage is written to help teenagers change their bad habits and live a healthy lifestyle. On the other hand, it provides us with a scientific way to identify and analyse our problems objectively, thus strengthening our resolve to tackle the seemingly common yet tough problems in our lives.) 【設計意圖】 步驟1旨在預測和驗證文章最后一段主要內容，梳理完整的語篇結構，步驟2旨在思考和討論作者的寫作目的。教師也可根據學生課堂反應情況融入對語篇人稱多次轉換的思考。
新人教版高中英語選修3Unit 4 Adversity And Courage教案
本活動旨在落實課時目標3。 The Student Union is looking for three students for a 3-week voluntary program in Guizhou province. The volunteers have got to be high school students, with a persevering personality and experiences in overcoming adversity. The volunteers need to stay, eat and teach with 20 pupils in a small school up on the hill of a village. There are no facilities but desks and a blackboard in the school. And there is no take-away food to be bought anywhere; the only way to feed yourself is to cook. You’re interested in applying. Write your application letter introducing what adversity you have ever overcome and how persevering you are as well as what you want to do when at work. Dear Student Union,【設計意圖】此任務旨在遷移一、二課時所學，解決實際問題。學生對比自己經歷過的挑戰(zhàn)或挫折，寫信給學生會申請前往貴州擔任短期支教教師，把個人以前是怎么戰(zhàn)勝挫折的經過書寫出來。結合所學，遷移創(chuàng)新，分析解決自身實際問題，在真實情境中學生通過仿寫進行主題語言的精確輸出。完成任務的過程中，能較多地使用已學語言、內容、結構和寫作手法來描述自己面對挫折的處理方式、態(tài)度和應有的品質，近一步激發(fā)學生樹立正確的價值觀，學會逆境出人才，堅忍不拔，從容不迫，又做到謙讓、分享和合作。課后學生修正習作，再次提交。
新人教版高中英語選修3Unit 5 Poems教案
本單元閱讀文本介紹了幾種簡單的英語詩歌形式，旨在讓學生能理解和欣賞英語詩歌的美，包括形式美、內容美、意義美，培養(yǎng)審美情趣，并從作品的意義美中獲得積極的人生態(tài)度和價值觀念啟示。 該文本是一則典型的說明性文本，用簡單易懂的語言向英語詩歌的初學者們介紹了五種比較簡單的英語詩歌形式。文題“A Few Simple Forms of English Poems”是整個文本的核心話題。正文內容共七段，按“總—分—總”建構。第一段為總起段，概述了英語詩歌的創(chuàng)作原因以及主要特點，涉及了形式、內容、意義等方面賞析英語詩歌的幾個主要維度；第二段至第六段分別介紹了童謠、清單詩、五行詩、俳句和唐詩五種英語詩歌形式；第七段收尾，鼓勵讀者嘗試英語詩歌創(chuàng)作。 在進行文本教學設計時，要引導學生梳理關于與詩歌要素和詩歌賞析有關的話題類語言，既包括format、rhythm、subject、image等名詞，也包括have a strong rhythm、be made up of、contain、consist of、convey這樣的動詞和動詞短語。
新人教版高中英語選修4Unit 3 Reaching Out Across the Sea教案
本活動旨在落實課時目標3。 Think about the following questions and talk about your own attitude in pairs.Q1: As for this topic，what impresses you the most in the passage?Q2: What do you think of the future of China’s further exploration in sea? Are you in favor of the further exploration？Why or why not? 【設計意圖】該活動是一個完全開放性的活動，每個學生都會有不同的答案。運用遷移所學，自由口頭表達自己對海洋探索的態(tài)度。對于中國海洋探索的未來，每個人的想法是不一樣的，有樂觀，有擔憂，有認為值得投入，也有認為不值得付出太大代價，這里給學生自由表達的空間只要學會有支撐自己觀點的事實就可以了，進一步培養(yǎng)學生批判性思維和正確的價值觀。 Assignment: 此任務旨在遷移一、二課時所學，培養(yǎng)學生辯證分析問題的能力。 Write about your idea of the future of China’s sea exploration. And add your attitude towards the effort China have made in sea exploration. You’re expected to use the language and the writing technique learnt in the passage.
人教版高中數學選修3二項式定理教學設計
二項式定理形式上的特點(1)二項展開式有n+1項,而不是n項.(2)二項式系數都是C_n^k(k=0,1,2,…,n),它與二項展開式中某一項的系數不一定相等.(3)二項展開式中的二項式系數的和等于2n,即C_n^0+C_n^1+C_n^2+…+C_n^n=2n.(4)在排列方式上,按照字母a的降冪排列,從第一項起,次數由n次逐項減少1次直到0次,同時字母b按升冪排列,次數由0次逐項增加1次直到n次.1．判斷(正確的打“√”，錯誤的打“×”)(1)(a＋b)n展開式中共有n項． ( )(2)在公式中，交換a，b的順序對各項沒有影響． ( )(3)Cknan－kbk是(a＋b)n展開式中的第k項． ( )(4)(a－b)n與(a＋b)n的二項式展開式的二項式系數相同． ( )[解析] (1)× 因為(a＋b)n展開式中共有n＋1項．(2)× 因為二項式的第k＋1項Cknan－kbk和(b＋a)n的展開式的第k＋1項Cknbn－kak是不同的，其中的a，b是不能隨便交換的．(3)× 因為Cknan－kbk是(a＋b)n展開式中的第k＋1項．(4)√ 因為(a－b)n與(a＋b)n的二項式展開式的二項式系數都是Crn.[答案] (1)× (2)× (3)× (4)√
人教版高中數學選修3全概率公式教學設計
2.某小組有20名射手，其中1，2，3，4級射手分別為2，6，9，3名.又若選1，2，3，4級射手參加比賽，則在比賽中射中目標的概率分別為0.85，0.64，0.45，0.32，今隨機選一人參加比賽，則該小組比賽中射中目標的概率為________. 【解析】設B表示“該小組比賽中射中目標”，Ai(i=1，2，3，4)表示“選i級射手參加比賽”，則P(B)= P(Ai)P(B|Ai)= 2/20×0.85+ 6/20 ×0.64+ 9/20×0.45+ 3/20×0.32=0.527 5.答案：0.527 53.兩批相同的產品各有12件和10件，每批產品中各有1件廢品，現在先從第1批產品中任取1件放入第2批中，然后從第2批中任取1件，則取到廢品的概率為________. 【解析】設A表示“取到廢品”，B表示“從第1批中取到廢品”，有P(B)= 112，P(A|B)= 2/11 ，P(A| )= 1/11所以P(A)=P(B)P(A|B)+P( )P(A| )4．有一批同一型號的產品，已知其中由一廠生產的占 30%, 二廠生產的占 50% , 三廠生產的占 20%, 又知這三個廠的產品次品率分別為2% , 1%, 1%，問從這批產品中任取一件是次品的概率是多少？
人教版高中數學選修3組合與組合數教學設計
解析:因為減法和除法運算中交換兩個數的位置對計算結果有影響,所以屬于組合的有2個.答案:B2.若A_n^2=3C_(n"-" 1)^2,則n的值為( )A.4 B.5 C.6 D.7 解析:因為A_n^2=3C_(n"-" 1)^2,所以n(n-1)=(3"(" n"-" 1")(" n"-" 2")" )/2,解得n=6.故選C.答案:C 3.若集合A={a1,a2,a3,a4,a5},則集合A的子集中含有4個元素的子集共有 個. 解析:滿足要求的子集中含有4個元素,由集合中元素的無序性,知其子集個數為C_5^4=5.答案:54.平面內有12個點,其中有4個點共線,此外再無任何3點共線,以這些點為頂點,可得多少個不同的三角形?解:(方法一)我們把從共線的4個點中取點的多少作為分類的標準:第1類,共線的4個點中有2個點作為三角形的頂點,共有C_4^2·C_8^1=48(個)不同的三角形;第2類,共線的4個點中有1個點作為三角形的頂點,共有C_4^1·C_8^2=112(個)不同的三角形;第3類,共線的4個點中沒有點作為三角形的頂點,共有C_8^3=56(個)不同的三角形.由分類加法計數原理,不同的三角形共有48+112+56=216(個).(方法二 間接法)C_12^3-C_4^3=220-4=216(個).
人教版高中地理選修1天體和星空教案
一、 天體1、 概念：宇宙間物質的存在形式。（聚集態(tài)的星體及星際物質）注：不作特殊交代的天體均指自然天體2、 幾種常見天體的觀察（指導學生閱讀課本，并總結講述學生自己平時的生活所見）3、幾種常見的天體恒星1） 定義：從質量、組成、形狀、發(fā)光與否等角度總結交代：數目多少（肉眼所見6000多顆）夜空里的點點繁星差不多都是恒星2)運動特點：（由恒星的“恒”字引發(fā)學生分析“北斗七星圖形變化”圖說明特點）結論：①恒星在不停的運動變化之中②相對位置似乎固定不變，故稱“恒星”3)光年----計量天體距離的單位（強調“距離”）分析知識點：①距離地球最近的恒星是 （8分鐘）(1. 5億公里)②距離地球次運的恒星是 (4.2光年)③現在能夠探測到的最遠天體距離地球多遠?星云（指導學生閱讀課本與恒星比較總結星云特點，可以從形態(tài)、質量、體積、密度、物質組成、觀察特點幾方面列表比較分析并小結）二、天體系統(tǒng)1、 概念：運動著的天體與天體之間相互吸引、相互繞轉而形成的不同級別的系統(tǒng)。
人教版高中地理選修1第一章第一節(jié)天體和天體系統(tǒng)教案
【概括】天體是在不斷的運動著的。運動著的天體互相吸引和互相繞轉，從而形成天體系統(tǒng)。【板書】四、天體系統(tǒng)【啟發(fā)】天體系統(tǒng)有大有小，大的天體系統(tǒng)又可包含許多小的天體系統(tǒng)。剛才同學們提到的三個天體系統(tǒng)之間是如何包含的呢？（銀河系含太陽系，太陽系含地月系）【掛圖講解】地月系只有兩個天體，地球和月球，它們之間的平均距離為384401千米；太陽系則包括太陽、九大行星、數十顆衛(wèi)星及其它天體，整個太陽系的直徑至少100億千米以上；而銀河系則擁有2000多億顆太陽恒星及恒星系統(tǒng)，包括了我 們用肉眼能看到的所有恒星，其主體部分的直徑達7萬光年，太陽就處于距銀河系中心2.3萬光年的位置上?！局v解】銀河系已如此龐大，是否 就是最大的天體系統(tǒng)呢？是否就是我們的宇宙呢？還遠遠不是。利用天文望遠鏡，我們可以觀測到在銀河系之外，還有約10億個類似的天體系統(tǒng)，它們被統(tǒng)稱為河外星系。
人教版高中地理選修1地球的早期演化和地質年代教案
學習方法實驗法、討論法。教學 媒體投影儀、投影片、巖石標本、實驗器具。學習過程一、地球的早期演化和地質年代1、思考回答：初生地球 有什么特點？2、【啟發(fā)提問】看課本大氣的早期是怎樣演化的？水圈是怎樣形成？ 學生分組討論后回答，相互啟發(fā)補充。3、學生討論、回答：生命起源的過程怎樣？大氣又是怎樣繼續(xù)演化的？二、記錄地球歷史 的“書頁 ”——巖層和化石1、學生討論 、回答：地球上巖漿巖、變質巖、沉積巖三種巖石的形成和特點2 5、【啟發(fā)提問】化石是怎樣形成的？他有什么作用？三、地質年代1、【啟發(fā)提問】地質年代劃分依據是什么？2、學生討論、總結。各階段的特點？學后記：
人教版高中地理選修1恒星的一生和宇宙的演化教案
①演示動畫，理解大爆炸宇宙論②主要觀點：? 大約150億年前，我們所處的宇宙全部以粒子的形式、極高的溫度、極大的密度，被擠壓在一個“原始火球”中。? 大爆炸使物質四散出擊，宇宙空間不斷膨脹，溫度也相應下降，后來相繼出現在宇宙中的所有星系、恒星、行星乃至生命。2、其它宇宙形成理¬——穩(wěn)定理論3、大膽猜測：宇宙的將來史蒂芬·霍金是英國物理學家，他提出的黑洞理論和宇宙無邊界的設想成了現代宇宙學的重要基石。霍金的宇宙無邊界的設想是這樣的：第一，宇宙是無邊的。第二，宇宙不是一個可以任意賦予初始條件或邊界的一般系統(tǒng)?；艚痤A言宇宙有兩種結局：永遠膨脹下去，不斷地擴大，我們將看到所有星系的星球老化、死亡，剩下我們孤零零的，在一片黑暗當中?；蛘邥s而在大擠壓處終結科學巨人霍金：探索的精神）