一期星 日七月八年二七九一届公年一十六國民華中
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八月十一 -
贊背乐游魔
八月四日至十六日
H
|慣將與人生:
‘八月七日:
八月十二日
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·新媒
·大仔戶外訓經营八月十日至十一日 九月十三日
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七月北四百至育,同右:
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KK】一九四四
大月何日至八日 八月八日十一日 八月一日至廿六日
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八月十一至十二日,
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八月十一日 一、八、十五日商右
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月七日, 〇八月八日至十二年
大月十一日
八月八日:
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日华营:
八月十二日至十” ·同右
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FU
同右:
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八月十二日至十三
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HOMEPOK
游中心
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八月十二二年
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H二三一七OK. :
二
REFERENCE LIBRARY
7 AUG 1972
ITY HAL
八月十二日
大月十一日
六月十一日,
聚 NTUK
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八月十日.
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同
·何
育教聞港頁一第張四第
日八廿月六年子壬磨宴 WAH KIU YAT PO
報日橋.
術
11.
七月四日至八月
八月八日至十一日
七月廿五日至八月
·商
辉
登望運淡
大月11日,
一大片六区。十三日
大下午二险——四
大月八日,十五日 八月八日——九日
八月八日二十日
「八月六日七日 }],廿九日
阿!
多模野餐
八月十一日
八月六日:
EUKI POK
泊爾股赛西.
中風
味香
·大網仔.
大網仔
八月十三至十三日:
八月十二日至十三6 *治心會服務團
k宄弍三八五
藍英七七一八九
KOK
[K六九九九
兄弟姊妹B·
- 李富青年中心.
GET.
·佩代
大月氏钻
K六八四七七
機
·本愛新出贯坐八月十日
市路 市政局乃香淑電。
H六〇〇九二
李书壑游泳汛
九月十一日:
心
∴、陰氣日製及民政司
丘六○○九八二滑役些演
送
大浪西津 | 大月攷日——七日
石煞尾新區一號,八月十二日, 長沙灣 猃樂塲 八月十二日
份出
·苴六一六九六一
,北台中
九月八日至
九月五日深六日
·荣大仙社區服務中心 八月七日至十八日中,和盤
九月十二日,
八月八日及十日,
| KOLㄤ一九
MEDIL THE
外营
任四五九〇一一年营
:元月號过至七日
「大月八日至十九日
八月七日
八月九日至十一日
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:
八月六日
. Hi弍一七六、
產、工、
及中心原体”
̇天文台、機場
八月十一日 . 面右
·油青中心
ENKI YOK
大拉京及大統西球 八月七日至八日開右
務中心!
大東社區服
|八月七日至十一日
!
抢救
屈想
EUR POK
◎ 游泳會,一四四,李水灣:
八月八日上午九時
全推就會於我雅
至下午四時坐
瑪利士丹利女童中心 HFC六 .
服些公司、巴
由八月十日上午九時
·H七一七八九五
·河姵髖跋、辛導
至于野,由下午上圖右,
品
五七二四四式
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若你致莳龠(九月七日薈九日
- 嘅雅各家背會
女悒年會大
山女青年營
九月八日照十日
·伊館及假頓、八月十二至十四日:
八月十二至十四日,同右
̇尔畴濍戶外工作
新界名勝古
八月八、九十十十一日同有
佐蚵
·砵蘭
·六月十二年
九月十一日
右右右
EKKOMIT
H二五一五六,滾
H3三一七〇六經已
: 西大學
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八月七日至十一月
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云港女童軍廳會八月七日至九日
八月十日至十二日...同右.
七
九月七日至十日 1 八月十七日至十七日
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五月七日至九日
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育僑華
中學同學暑期後個欄
趣味數學
(-)
Riddles in Mathematic
(1) Trisecting an angie
The trisection of an angle by
uler and compass alone is in gen= eral impossible. Of course, there are angles, such as 900 and 180° for which the trisection can be performed: What we have to show ds that the trisection cafinot be effected by a procedure valid for Fevery angle. For the proof, it is.
quite sufficient to. exhibit only one angle that cannot be trisected; since a valid general method woulà have to cover every single example. Hence the non-existence of a gen- eral method will be proved if we can demonstrate, for example, thay the angle 60° cannot be trisected: hu uler and compass alone. LOWe can obtain an algebraicy equivalent of this problem in dif-s ferent ways; the simplest is to con sider an angle o given by ite
cosine: Cos 0 = a. Then the pro-T blem is equivalent to that of find- ing the quantityie =
By a
simple trigonometrical formula, the with that
covine.of § is; connected
ofoby the equatior Cock = 2 = 40083 (5) 3C (E
In other words, the problem of secting the angle O with Cos = a amounts to constructing a solutione if the cubic equation
600 Equation
To show that this cannet. Lone in general, we take 9 so that g =cos 600 (1) then becomes
1823 – 6z =
+(2)
Then by a theorem that "If cubic equation with rational coef. ficients has no rational root, then none of its roots is constructiole from the rational field.", we need only show that this equation has n rational root. Let v 22, then (2) becomes Th
(3)
If there were a rational num-
berry = r/s:satisfying this equan"
tion, where rands are integers.
without common factor longer than
墨
1. we would have r-
From this it follows that s3 = r(r2
3s2) is divisible by
ry which means that rand s have.
a common factor unless r =
Inkewise s is a factor of
= 8 (s + 3x) which means that
rx and s have a common factor unless seat. since we assumed that r.and s had no common factor, we have shown that the only rational numbers which could possibly satisf By substituting (3) are + 1oz -1"
+1 and 1 for v in (8), we see that: neither value satisfies'it. Hence (3) arid consequently (2) has no rational root and the impossibilit of trisecting the angle is proved The theorem that the general angle cannot be trisected with ruler and compass alone is true only when the ruler is regarded as an instrument for drawing a straigr line:through any two given pointe and nothing else. By permitting other uses of ruler, the method of Archimedes provides a solution for, Frisecting an engler.
Dêt an arbitrany angle ribe: Lvern: Bxtend the base of the igle to the lefty and draw a sem. ircle with O as centre and arbitr ury radius r. Mark two points: A. und Bon the edge of the ruler. Such that AB = r, Keeping the g coint B on the Sémicircle, slids che ruler into the position where A lies on the extended base of the ingle x, while the edge of the
uler passes through the intersec- tion of the terminal side of the angiex with the semicircle about 9. With the ruler in this positio
raw a straight line, making an angley with the extended base or the original angle x..
It leaves as an exercise for the readers to prove that y=x.
暑期進修專欄
英文數學
"Tako 2987 from: 3875).
ENGLISH MATHEMATICS
28-1972
LESSON TWO
"SUBTRACTION.
called "us", Reane
| SOLUTION: The required differesion
2004 - 3875 = 2987 - 088-
ASSWER: The required difference-18-378
Whay saline difference between five thousand six hundred and thigh
Tour, and-three thousand) seyen, hundris and five? SOLUTION: The required difference - 563 - jog a ANSWER: The required difference is 1929 - Example. 2.
thouse?
twenty-sic to:
SOLUTIONS. The required value:- 10000 = 3036 = 6205 ANSWER: 6074 mustike added to 3025 to mine 10000
Example
There are 14,972, books in a school library bad 7,685 Tonka MPA va
Voidon and but took are atd. How many backs aru stilk ANG the library?.
SOLUTION The number of books which are still in the Library
1 34872, +17605 261-26826**
ANSWER: • 20,820 books are still an the school Jabenrya Example. 5
A bin filled with pit veighs & 25. 5/02, the tán vefphs à
Find there “yesight of oil. SOLUTION The required her weight
-416, 3 D ..7 2. ANSWER: The required net weight of wil Example. 6
Example
SOLUTION:
off
Find the difference between 15 yễ. 1 ft. 7 in, and 8 yd. 2 ft. 15 In
SOLUTION The required difference
10 lyd, 1 Ft., 7. inu – 8 yd. 2,602 11
ANSWER: The required difference is 7 yd. ft
(1) Take-4862 from 16:52.
EXERCISE 3
· (2), What is the difference between lit thousand, five
hundred and forry-seven and five thousand and, eighết Fill in the pissing figurens
口
(6)
597
12 pasuls 41 catties:- 3. picule 62 carties 11 tacl
Spiculs aris 6(7) 12 xq, yd. 9 mqj. £ts, 72-64.in - 6 nga pa.
á(9) 8 gallone Lipinta – 3 pallens 7 pinça
(7)qy
5(10)
4610) 4 watch stopped at quarter to (5145) in the
starred again at half past eight in the same day Por How long way it not going?" (11) The total weight of three sins of liquid is 13 269 7°c
If the first tan of de high & lb. Bax, and the second- weigh 22b. 6os. that as the weight of the third one?.
(11)
4(12) The length of 3 sticks van 128 yds. 1 Tt. 8 in. “TË"the".
lensch at the trai kich Nha Tử vi 20 an, and the read one was 20 yd, 2 sti What is the length of the third one?
(12)
...
"a (13) One side of a rectangle 3× 25:1, long. The whale distance
round is 160 Ft. Find the length of the longer side. *(24) from a
place
Pof cloth 5 cheung 5 chek long, a length
5 chek 6 ohuen as aút away, that length is left?
The total weight of 3/
Y parcels in 5 tone 2 cut." & Th..
the first one weight 3 tons to cut 2 16.492, and the
16) What fa'the difference befuson 3 tonn 12.cvt. 62 15.
2 x 11.79 . ?:
(17) Find the difference belucon 22 piculs 3 catifes G taula
(18) 16 cona 2015,5 tons 2 cutý 8:, - 12 cut. 8 lb. 9 oz. • ?
Yample 1
MULTIPLICATION
Multiply eight hundred and ninety-four by SOLUTION The required product = 894. x 6- NSWER: The required product is 5364 **
apply. Zv
There were four booke. Each had 8 pictures,
There altogether in these 4 books? SOLUTION The required number of picture ANSKER The required number of pictures
ple 3
A-woman work everyday in the week, a
she work in eighteen, weeks? SOLUTION. The required number of days
(7:1) 18 x 6108 worka Sn 100'days
ample.
Sunday Bor
a family drinks 3 pints of pilk everyday's How
drink in 8 work?
SOLUTION The required number of gall
3.x 87 (pinta) → 168 (pinza) A
ANSWER They deank 21 gallons of milk in 8 socken
I catty of pork conta $3.29. How much would eattles 8. Lorie cost
SOLUTION The required total cost $3.20
ANSWER: The required total cost is $11,20
ample 6
Find the total age of atx boys. If the average age of the first innes
16 16, the average age of the next-tva: 1a 15 and the sixth one is
SOLUTION: The Aquiraz tatak ugasi (3 x 18 » 2
ANSWER The required total age. is 91 years,
EXERCISE
(1) How many gallons of milk are needed to 48 half-pint hotties.
(2) A postman cycles 33 miles every day 1le does not work on Sunday
How many ralles does he cycle in five weeks?
(3) A driver takes 16 minutes 10 seconds to side round a racing track, liha- travels as this speed for rounds of the track, how long will he take (4) One pound of beef costs 32.80 How much would 5 lb. 02, rosi? 45) Find the sum and product of the following numbers, 8, 15, 20 and 24%9 (6) A family uses 60 cattles of rice each month; if the price of rice is $60
picut for the period from January to March, $64 from April to August, und 561 from September to December, how nitch is spent on nice for the whole year?, AN
(C). If a car travels #1,30 mies per hour, how long will it take to travel 250 miles! (8) A' giri-Bought 3 books at $1:30 per book, 400 sheets of writing paper as
80 per hundred and Srulers at 40 each. How much did she pay together? [(9) Tea A costs 80 cents an ounce and tea:8 $1.00 a lat. What is the
difference in price per pound? 46 ounces = 12 (aeks)
(10).A is 4 inches taller than.B. Two years ago he was & inches taller than B. If A. Kas grown 2 Inches in this tine, how much has B. grown? 你
(11) One day a man, bought 20 dozen of eggs at $3.60 per dozen. The next
day the price. had decreased by. Sc per eng How many dozenfone
d he now buy with same amount of money?
(12) A father is 32 year older than his son. The son is 4 years older than his Sister. If the mother is 6 years younger than the father, by how many
Eyears ba (the mother adder that the daughter?
(13) It 1 pion of water welshe 10 pounds, what is the weight of 1 pint of waterh (14) Bucket A contains 4 pints of a liquid and bucket 8.4 pints of water. L punt of the liquid is poured from A into B, and is mised well: pint of the mixture is then poured from Binio A. How much water is now la bucket A?
One day a man (bolight 70 pounds of oranges at $1.20/2 pound. The
next day the price had increased by 20 cents per pound. How many!
pounds could he now buy with the same sum of money?