騰訊科技訊(Everett/編譯)據國外媒體報道﹐近日考古學家在保加利亞發掘出兩個中世紀人類骨架﹐離奇的是骨骸胸前被鐵棍戳穿了﹐這一詭異的現象使人想起了吸血鬼的傳說。在歐洲西部和中部地區的流傳著關於人死後變成吸血鬼的故事﹐當時的人們對此深信不疑﹐而該墓室中的兩具骨架胸前穿透了鐵棍就是防止他們變成吸血鬼。根據考古學家們測定﹐兩具骷髏的年代可追溯到800年前﹐其具體的地點位於保加利亞的黑海之濱索佐波爾(Sozopol)鎮上。根據保加利亞民族史博物館的負責人博日達爾季米特洛夫(Bozhidar Dimitrov)介紹﹕『這兩具胸前被鐵棍戳穿的骷髏在保加利亞的一些村莊中還是很普遍的埋葬方式﹐但是該現象直到20世紀第一個十年後就很少出現了。』從異教信仰的角度看﹐有些人認為生前幹壞事的人在死後會變成吸血鬼﹐因此死後需要用鐵棍或者木棍將胸前刺穿再埋葬。之所以將棍子類物體穿透骷髏﹐是因為當時人們認為棍子會阻礙它們離開墳墓﹐防止在午夜失蹤。歷史學家季米特洛夫統計﹐在多年來的發掘工作中﹐大約有100具屍骨的胸前被穿刺﹐防止它們變成吸血鬼。但是令季米特洛夫不能理解的是﹐為什麼一個普通的考古發現會變得如此流行﹐受到了各界的關注﹐也許是因為吸血鬼這個詞將這些普通的墓葬變得極為神秘。
季米特洛夫認為當時人們覺得會變成吸血鬼的一般是貴族和神職人員﹐但奇怪的是其中並沒有發現女性屍骨﹐可能是當時的人們並不害怕女巫。就在上個月﹐意大利的考古人員發現了一具下巴被磚頭塞住的屍骨﹐據瞭解這具屍骨的年代可追溯到16世紀﹐當時爆發了瘟疫﹐因此人們認為在死去的人嘴中塞入磚頭防止它們變成吸血鬼。佛羅倫薩大學人類學家馬泰奧博里尼(Matteo Borrini)在對一座小島的調查後發現﹐諸如黑死病等死亡瘟疫蔓延的背後都有關於吸血鬼的傳說。
在1300年至1700年間﹐瘟疫在歐洲大陸上此起彼伏﹐這段時間也是吸血鬼傳說發展到高潮的時期﹐其中也有當時的人們對屍體的自然分解並不瞭解的因素﹐比如有人將已經埋葬的墓室重新打開﹐就發現屍體的器官變得臃腫﹐而且頭髮仍然在生長﹐血液會從口中滲出﹐因此人們相信這些死去的屍體還活著。為了不使它們變成吸血鬼傳播瘟疫﹐人們就用磚頭塞住它們的嘴巴。
A skeleton pierced with a piece of iron is seen on display during a media event at the National History Museum in Sofia June 14, 2012. The museum plans to display a "vampire" skeleton on Saturday after unearthing the 700-year-old remains of two men stabbed through the chest with iron rods. Archaeologists, excavating a monastery near the Black Sea city of Sozopol, discovered the skeletons, which were buried in a pagan ritual that they said was aimed at keeping the men from turning into vampires.(Photo: Reuters) Romania has long held claim to the vampire tourism title, owing to Bram Stoker's famous 1897 novel Dracula, set in the Romanian countryside of Transylvania. While a work of fiction, Dracula nonetheless had its roots in Romanian history and historical tales of vampires.
If Bulgaria has its way, it may be hoping its latest find helps draw some of those tourist dollars away from Romania, and into the museums, hotels, and restaurants of Bulgaria.
Unearthed last week in the Bulgarian Black Sea port town of Sozopol were two 700-year-old skeletons with iron rods thrust through their chests. This practice was performed on anyone considered to be a vampire or who had the potential to return to life as a vampire, and was still in use as late as the early 19th century.
This was a pagan belief widespread in the Bulgarian lands in the 12th to 14th centuries. People were very superstitious then," National History Museum director Bozhidar Dimitrov said.
"Throughout the country we have found over 100 such 'vampire' burials of mainly noblemen from the Middle Ages who were branded bloodsucking immortals."
Given the current popular culture craze with anything vampire related, it's not surprising that the discovery has already attracted global attention. Quick to capitalize on this discovery and attention, The Natural History Museum in Sofia will put one of these skeletons on display beginning June 16, with Dimitrov saying he expects a large turnout for the display.
Legends of vampires remain prevalent in many of the Balkan countries, and there have been reports that some people in Sozopol, where the two skeletons were discovered, have been having trouble sleeping at night since the discovery.
Of course there's nothing to indicate the skeletons were actually vampires, no doubt to the dismay of many. They were simply subjected to a pagan ritual to ensure they would not become one.
Still, for anyone interested in the history and legends of vampires, it's an intriguing discovery, and one that should prove to be a boon for the Bulgarian tourism industry.
A couple of weeks ago, news brokethat archaeologists in the Bulgarian Black Sea resort town of Sozopol had unearthed the skeletal remains of two men whose corpses had been stabbed with iron rods to prevent them from rising up and feasting upon the blood of the living. An iron ploughshare was still in one grave, piercing the rib cage of the would-be revenant. An iron implement was also left behind in the second skeleton but in his abdomen, which has considerably less lore-appeal, so he hasn’t gotten as much attention as the other one.
They were found buried in the necropolis of the St. Nicolas the Miracleworker monastery. (That’s according to the National Museum of History in Sofia; this article says the necropolis was outside the church of Saints Cyril and Methodius, a church very much in the public eye right now as the host of the purported bones of John the Baptist which were discovered on the island of St. Ivan in 2010. The bones have recently been dated to the first century A.D., and DNA testing confirmed that they’re all from the same Middle Eastern man. Cue the inevitable St. John hysteria.)
The skeletons date to between the 12th and 14th centuries. The fellow with the ploughshare jammed in his chest was buried near the apse of the church, an indication that he was an important figure. Iron was used to pierce the corpses of the wealthiest men while wood was used for the less wealthy, but all the people deemed to be potential vampires were powerful, influential men in life. Clerics, civic leaders, aristocrats, intellectuals: if they were cruel and abusive with their gifts when they were alive, their souls would not ascend to heaven but would remain in their rotting corpses, driving them to rise from the grave to terrorize y’all’s neighborhood.
Archaeologists have a theory about who this particular scoundrel might have been.
Bulgarian historians believe that the vampire grave most likely belong [sic] to one of the medieval mayors of Sozopol. The man’s name was Krivich, and he is known to have had a background as a pirate and bandit who exemplified evil for the town which was part of both the Bulgarian Empire and the Byzantine Empire in the Middle Ages.
“He demonstrated incompetence when defending the town from a siege. As a result, Sozopol was overrun by the Genoese who took everything away from the local residents,” [Professor Bozhidar Dimitrov, head of the Bulgarian National History Museum,] said.
I’m not sure what their grounds are for this speculation, other than the generally appropriate date (Krivich failed to protect the city from Genoese troops in the 14th century) and the plum burial spot indicating he was a man of importance, but still, medieval vampire pirate mayor …. That’s the kind of cool that cannot be denied.
The remains of 100 vampire-treated people, all of them men, all of them prominent citizens, have been found in Bulgaria. These two are the first ever discovered in Sozopol, a tiny fraction of the 700 graves unearthed in the necropolis. Most of them have been reburied, as will the Sozopol skeleton with the iron stomach. The one sporting the ploughshare in his chest, on other hand, has been sent to Sofia to go on display at theNational Museum of History. It will become part of a permanent exhibit on medieval Bulgarian folklore.
It’s tourist season, you see, and vampires are big business. Already thousands of people from Germany, Britain, Russia and the US are flocking to Sozopol to catch a glimpse of a vampire skeleton in situ. Souvenir stores are stocking up on truly awful Dracula mugs and t-shirts; “vampire steaks” and “vampire cocktails” have sprung up on menus all over town. Just to pin down the cheeseball tourism trade like it’s a dead evil nobleman, Sozopol also has plans in the works to become twinned with Sighisoara, Romania, the birthplace of Vlad III, Prince of Wallachia, aka Vlad the Impaler, aka Dracula.
同時也有10部Youtube影片,追蹤數超過6萬的網紅Herman Yeung,也在其Youtube影片中提到,電子書 (手稿e-book) (共261頁) (HK$199) https://play.google.com/store/books/details?id=Fw_6DwAAQBAJ Calculus 微積分系列︰ https://www.youtube.com/playlist?list=PLz...
「fraction practice」的推薦目錄:
- 關於fraction practice 在 劉天賜個人專頁 Facebook 的最佳貼文
- 關於fraction practice 在 Herman Yeung Facebook 的精選貼文
- 關於fraction practice 在 Herman Yeung Youtube 的最佳解答
- 關於fraction practice 在 Herman Yeung Youtube 的最佳貼文
- 關於fraction practice 在 Herman Yeung Youtube 的最佳貼文
- 關於fraction practice 在 Let's Practice a few EASY Fraction Problems…… 的評價
- 關於fraction practice 在 Math fractions, Fraction practice, Fractions worksheets 的評價
fraction practice 在 Herman Yeung Facebook 的精選貼文
Form 6 Maths - M2 - Practice Paper
SECTION A
Question 1
屬中五程度的 binomial theorem 二項式定理,仲要係最容易個隻。
Question 2
System of linear equation 線性方程組 之 homogeneous equation 齊次三元
有 non-trivial solution 非零解,其實只係
而同學細心d睇,其實係一個2次的狀態,
只需要用產產產的方法就 okay
Question 3
會考程度的 MI,相對比較繁少少的考法
時間會長少少,不過 5 分,所以 format 上不要太過求其
Question 4
(a) part 唔難,
但 (b) part 其實係 partial fraction (積分 integration 教過的技巧。)
Question 5
(a) part 為 三角學的 compounded angle formula
而 (b) part 當中就算唔識計,都可以用到我地 program 黎估到答案係 0
Question 6
典型的 first principle 考法
Question 7
有d似中七 maths and statistics 的作風,利用 e 及微分 differentiation 砌公式出黎。
Question 8
(a) 正如上堂所講 substitution 唔會再俾 hint (除非太深)
(b) 積分A筆記已列曬所有 by part 的典型題目,呢條係其中一條
Question 9
Tangent, normal 切線法線 的第三類題型,溫翻我地d筆記無可能唔識。
Question 10
(a) 開始有少少睇頭,要自己明白要 in 都 e 就一定要次方同d裡面果件完全相同先可以 in 到。開始超越中五程度
(b) 開始打破傳統,迫學生用 shell method,仲要完全明白內裡 concept 先計到。
我地會於 intensive plan b 加強呢 part 的技巧
大睇上 section A 要攞分唔算太難,如果數學底較差的同學,應該放多D時間嚮上面,令自己可以當中取得40分以上,就一定穩合格
SECTION B
Question 11
(a), (b) 唔算難,但 (c) part 就要睇你有無做過 past paper,其實有某幾年的 past paper 都有類似考法,有做過的相信用多少少時間應該攻得入,無做過的可能真係會全軍覆沒。
Question 12
(a)(i) & (a)(ii) part 其實都係用緊中五程度的 2D Vector
(a)(iii) part 就要你好明白立體向量的概念,如果學校教得好少或者好亂,可能完全唔知佢問咩。
(b)(i) 有背公式唔難搵
(b)(ii) 的確好深,要明白如何運用平行於抽象的3D當中,此 part 的深度已達中七。
Question 13
(a) 要了解 odd, even function 奇偶函數的特性,否則無可能識計
(b) 利用 compounded angle formula 複數公式,慢慢砌一定砌到,但2分的回報實在太低。
(c) 要用曬 (a), (b) part 的結果,當中都算複雜
Question 14
(a) part 好淺
(b) part 的內在 concept 唔難,但好煩,好易令自己陷入困境而浪費好多時間
綜合全份卷,都係算深,但部署上一定要先做 section A,
section A係50分,section B又係50分,
但所用的時間相信 section B要多一倍
成本效益,所以一定先攻陷 section A
另外 Long question 都係以取易不取難的戰術
做曬所有易食的部分。
fraction practice 在 Herman Yeung Youtube 的最佳解答
電子書 (手稿e-book) (共261頁) (HK$199)
https://play.google.com/store/books/details?id=Fw_6DwAAQBAJ
Calculus 微積分系列︰ https://www.youtube.com/playlist?list=PLzDe9mOi1K8o2lveHTSM04WAhaGEZE7xB
適合 DSE 無讀 M1, M2,
但上左 U 之後要讀 Calculus 的同學收睇
由最 basic (中三的 level) 教到 pure maths 的 level,
現大致已有以下內容︰
(1) Concept of Differentiation 微分概念
(2) First Principle 基本原理
(3) Rule development 法則證明
(4) Trigonometric skills 三角學技術
(5) Limit 極限
(6) Sandwiches Theorem 迫近定理
(7) Leibniz Theorem 萊布尼茲定理
(8) Logarithmic differentiation 對數求導法
(9) Implicit differentiation 隱函數微分
(10) Differentiation of more than 2 variables 超過2個變數之微分
(11) Differentiation by Calculator 微分計數機功能
(12) Application of Differentiation - curve sketching 微分應用之曲線描繪
(13) Meaning of Integration 積分意義
(14) Rule of Integration 積分法則
(15) Trigonometric rule of Integration 三角積分法則
(16) Exponential, Logarithmic rule of integration 指數、對數積分法則
(17) Integration by Substitution 代換積分法
(18) Integration by Part 分部積分法
(19) Integration Skill : Partial Fraction 積分技術︰部分分式
(20) Integration by Trigonometric Substitution 三角代換積分法
(21) t-formula
(22) Reduction formula 歸約公式
(23) Limit + Summation = Integration 極限 + 連加 = 積分
(24) Application of Integration – Area 積分應用之求面積
(25) Application of Integration – Volume 積分應用之求體積
(26) Application of Integration – Length of curve 積分應用之求曲線長度
(27) Application of Integration – Surface area 積分應用之求表面積
(28) L’ Hospital rule 洛必達定理
(29) Fundamental Theorem of Integral Calculus 微積分基礎原理
(30) Calculus on Physics 微積分於物理上的應用
(31) Calculus on Economics 微積分於經濟上的應用
(32) Calculus on Archeology 微積分於考古學上的應用
之後不斷 updated,大家密切留意
------------------------------------------------------------------------------
Pure Maths 再現系列 Playlist: https://www.youtube.com/playlist?list=PLzDe9mOi1K8os36AdSf64ouFT_iKbQfSZ
------------------------------------------------------------------------------
Please subscribe 請訂閱︰
https://www.youtube.com/hermanyeung?sub_confirmation=1
------------------------------------------------------------------------------
HKDSE Mathematics 數學天書 訂購表格及方法︰
http://goo.gl/forms/NgqVAfMVB9
------------------------------------------------------------------------------
Blogger︰ https://goo.gl/SBmVOO
Facebook︰ https://www.facebook.com/hy.page
YouTube︰ https://www.youtube.com/HermanYeung
------------------------------------------------------------------------------
fraction practice 在 Herman Yeung Youtube 的最佳貼文
電子書 (手稿e-book) (共261頁) (HK$199)
https://play.google.com/store/books/details?id=Fw_6DwAAQBAJ
Calculus 微積分系列︰ https://www.youtube.com/playlist?list=PLzDe9mOi1K8o2lveHTSM04WAhaGEZE7xB
適合 DSE 無讀 M1, M2,
但上左 U 之後要讀 Calculus 的同學收睇
由最 basic (中三的 level) 教到 pure maths 的 level,
現大致已有以下內容︰
(1) Concept of Differentiation 微分概念
(2) First Principle 基本原理
(3) Rule development 法則證明
(4) Trigonometric skills 三角學技術
(5) Limit 極限
(6) Sandwiches Theorem 迫近定理
(7) Leibniz Theorem 萊布尼茲定理
(8) Logarithmic differentiation 對數求導法
(9) Implicit differentiation 隱函數微分
(10) Differentiation of more than 2 variables 超過2個變數之微分
(11) Differentiation by Calculator 微分計數機功能
(12) Application of Differentiation - curve sketching 微分應用之曲線描繪
(13) Meaning of Integration 積分意義
(14) Rule of Integration 積分法則
(15) Trigonometric rule of Integration 三角積分法則
(16) Exponential, Logarithmic rule of integration 指數、對數積分法則
(17) Integration by Substitution 代換積分法
(18) Integration by Part 分部積分法
(19) Integration Skill : Partial Fraction 積分技術︰部分分式
(20) Integration by Trigonometric Substitution 三角代換積分法
(21) t-formula
(22) Reduction formula 歸約公式
(23) Limit + Summation = Integration 極限 + 連加 = 積分
(24) Application of Integration – Area 積分應用之求面積
(25) Application of Integration – Volume 積分應用之求體積
(26) Application of Integration – Length of curve 積分應用之求曲線長度
(27) Application of Integration – Surface area 積分應用之求表面積
(28) L’ Hospital rule 洛必達定理
(29) Fundamental Theorem of Integral Calculus 微積分基礎原理
(30) Calculus on Physics 微積分於物理上的應用
(31) Calculus on Economics 微積分於經濟上的應用
(32) Calculus on Archeology 微積分於考古學上的應用
之後不斷 updated,大家密切留意
------------------------------------------------------------------------------
Pure Maths 再現系列 Playlist: https://www.youtube.com/playlist?list=PLzDe9mOi1K8os36AdSf64ouFT_iKbQfSZ
------------------------------------------------------------------------------
Please subscribe 請訂閱︰
https://www.youtube.com/hermanyeung?sub_confirmation=1
------------------------------------------------------------------------------
HKDSE Mathematics 數學天書 訂購表格及方法︰
http://goo.gl/forms/NgqVAfMVB9
------------------------------------------------------------------------------
Blogger︰ https://goo.gl/SBmVOO
Facebook︰ https://www.facebook.com/hy.page
YouTube︰ https://www.youtube.com/HermanYeung
------------------------------------------------------------------------------
fraction practice 在 Herman Yeung Youtube 的最佳貼文
電子書 (手稿e-book) (共261頁) (HK$199)
https://play.google.com/store/books/details?id=Fw_6DwAAQBAJ
Calculus 微積分系列︰ https://www.youtube.com/playlist?list=PLzDe9mOi1K8o2lveHTSM04WAhaGEZE7xB
適合 DSE 無讀 M1, M2,
但上左 U 之後要讀 Calculus 的同學收睇
由最 basic (中三的 level) 教到 pure maths 的 level,
現大致已有以下內容︰
(1) Concept of Differentiation 微分概念
(2) First Principle 基本原理
(3) Rule development 法則證明
(4) Trigonometric skills 三角學技術
(5) Limit 極限
(6) Sandwiches Theorem 迫近定理
(7) Leibniz Theorem 萊布尼茲定理
(8) Logarithmic differentiation 對數求導法
(9) Implicit differentiation 隱函數微分
(10) Differentiation of more than 2 variables 超過2個變數之微分
(11) Differentiation by Calculator 微分計數機功能
(12) Application of Differentiation - curve sketching 微分應用之曲線描繪
(13) Meaning of Integration 積分意義
(14) Rule of Integration 積分法則
(15) Trigonometric rule of Integration 三角積分法則
(16) Exponential, Logarithmic rule of integration 指數、對數積分法則
(17) Integration by Substitution 代換積分法
(18) Integration by Part 分部積分法
(19) Integration Skill : Partial Fraction 積分技術︰部分分式
(20) Integration by Trigonometric Substitution 三角代換積分法
(21) t-formula
(22) Reduction formula 歸約公式
(23) Limit + Summation = Integration 極限 + 連加 = 積分
(24) Application of Integration – Area 積分應用之求面積
(25) Application of Integration – Volume 積分應用之求體積
(26) Application of Integration – Length of curve 積分應用之求曲線長度
(27) Application of Integration – Surface area 積分應用之求表面積
(28) L’ Hospital rule 洛必達定理
(29) Fundamental Theorem of Integral Calculus 微積分基礎原理
(30) Calculus on Physics 微積分於物理上的應用
(31) Calculus on Economics 微積分於經濟上的應用
(32) Calculus on Archeology 微積分於考古學上的應用
之後不斷 updated,大家密切留意
------------------------------------------------------------------------------
Pure Maths 再現系列 Playlist: https://www.youtube.com/playlist?list=PLzDe9mOi1K8os36AdSf64ouFT_iKbQfSZ
------------------------------------------------------------------------------
Please subscribe 請訂閱︰
https://www.youtube.com/hermanyeung?sub_confirmation=1
------------------------------------------------------------------------------
HKDSE Mathematics 數學天書 訂購表格及方法︰
http://goo.gl/forms/NgqVAfMVB9
------------------------------------------------------------------------------
Blogger︰ https://goo.gl/SBmVOO
Facebook︰ https://www.facebook.com/hy.page
YouTube︰ https://www.youtube.com/HermanYeung
------------------------------------------------------------------------------
fraction practice 在 Math fractions, Fraction practice, Fractions worksheets 的推薦與評價
Sep 13, 2014 - Help your fifth grader master fractions with these printable, easy-to-follow fraction worksheets. ... <看更多>
fraction practice 在 Let's Practice a few EASY Fraction Problems…… 的推薦與評價
Math help with basic fractions to include adding fractions, subtracting fractions, multiplying fractions and dividing fractions. · Math Notes: ... ... <看更多>