1972-08-07 — Page 13

一期星 日七月八年二七九一届公年一十六國民華中

本港

新聞

凰

全港青年暑假康樂活動

养

八月八日

元丹沉至七日

問問

八月六日至十二日一個節目

九月七至九日

八月十二至十四日

耐越

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

·飛 新界

·新媒

·大仔戶外訓經营八月十日至十一日 九月十三日

HUNTPOK

大麻子中心

祖油餅股務,

NT六六五七 伏兵義四一四一

ENYOK

七月北四百至育,同右:

大宮

大月十一日

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

树开

八月十一至十二日,

八万八日至八月十

航機

蓉蒻

八月十一日 一、八、十五日商右

向右

第一期被台额:陈风女子中学

月七日, 〇八月八日至十二年

大月十一日

八月八日:

沿社會服務 會

日华营:

八月十二日至十” ·同右

八月十二日

FU

同右:

•H二一七〇六

「見文倍,

八月十二日至十三

辣酱

電話裡會務推

HOMEPOK

游中心

大坑東蕤服

東九〇一九一九

EMIL

八月十二二年

·西亞地青年中心: : Kü一六五七一

·八月士日至十

八月十二日

大同五月至七日

SONLINE

少年色潤&

劉南宁年中心 - 全港社會服務聯會

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

.0

八月十日.

NT11六四

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

:

:

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

EX

[凝^B

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

. 小組分酸蛋

日

11 POK

1月日月月月月月月

十九九

E! POK

四四

K八八一九九一兒好營

-石硤尾短文小學

八月七日至十一月

旗邦

見永識

·崇督學校東頭村

K

八月五日至七日

月七日至廿一日

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

八月七日至九日

五月七日至九日

八月八日至八月十

左右右右右右

·突社紅社

魚服字服

挥诃涼州村服翾中心,H究大五七七八

好爽好切會

$1$88

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?