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Getalpatrone

In vorige jare het jy patrone gesien in die vorm van prentjies en getalle. In hierde hoofstuk sal ons meer leer van die wiskunde van patrone. Patrone is herkenbaar as herhalende reekse wat gevind kan word in die natuur, vorms, gebeure, groepe van getalle en op baie ander plekke in ons daaglikse lewe. Byvoorbeeld, patrone kan gevind word in die sade van sonneblomme, sneeuvlokkies, geometriese patrone op lappieskomberse en teëls en reekse getalle soos 0; 4; 8; 12; 16; ...

Ondersoek : patrone

Kan jy die patrone herken in die volgende reekse van getalle?

  1. 2; 4; 6; 8; 10; ...
  2. 1; 2; 4; 7; 11; ...
  3. 1; 4; 9; 16; 25; ...
  4. 5; 10; 20; 40; 80; ...

Algemene getalpatrone

Reekse van getalle kan interessante patrone bevat. Die volgende is ʼn lys van die mees algemene patrone en hoe hulle gevorm word.

Voorbeelde:

  1. 1 ; 4 ; 7 ; 10 ; 13 ; 16 ; 19 ; 22 ; 25 ; . . . Hierdie reeks het ʼn verskil van 3 tussen al die getalle. Die patroon word gevorm deur elke keer 3 by te tel by die vorige getal.
  2. 3 ; 8 ; 13 ; 18 ; 23 ; 28 ; 33 ; 38 ; . . . Hierdie reeks het ʼn verskil van 5 tussen al die getalle. Die patroon word gevorm deur elke keer 5 by te tel by die vorige getal.
  3. 2 ; 4 ; 8 ; 16 ; 32 ; 64 ; 128 ; 256 ; . . . Hierdie reeks het ʼn faktor van 2 tussen al die getalle. Die volgende getal in die reeks word gevorm deur die vorige een met 2 te vermenigvuldig.
  4. 3 ; 9 ; 27 ; 81 ; 243 ; 729 ; 2187 ; . . . Hierdie reeks het ʼn faktor van 3 tussen al die getalle. Die volgende getal in die reeks word gevorm deur die vorige een met 3 te vermenigvuldig.

Spesiale reekse

Driehoeksgetalle

1 ; 3 ; 6 ; 10 ; 15 ; 21 ; 28 ; 36 ; 45 ; . . .

Hierdie reekse word gevorm deur ʼn patroon van kolletjies wat ʼn driehoek vorm. Deur nog ʼn ry kolletjies aan te heg (waar die elke nuwe ry een meer kolletjie bevat as die vorige een) en die kolletjies te tel, is dit moontlik om die volgende getal in die reeks te vind.

Vierkantsgetalle

1 ; 4 ; 9 ; 16 ; 25 ; 36 ; 49 ; 64 ; 81 ; . . .

Die waarde van ʼn term in die reeks word gevind deur die posisie (pleknommer in die ry) te kwadreer. Die tweede getal in die reeks is 2 kwadraat ( 2 2 o f 2 × 2 ). Die sewende getal is 7 kwadraat ( 7 2 o f 7 × 7 ) ens.

Derdemagsgetalle

1 ; 8 ; 27 ; 64 ; 125 ; 216 ; 343 ; 512 ; 729 ; . . .

Die waarde van ʼn term in die reeks word gevind deur die posisie tot die derde mag te verhef. Die tweede getal in die reeks is 2 tot die mag 3 ( 2 3 o f 2 × 2 × 2 ). Die sewende getal in die reeks is 7 tot die mag 3 ( 7 3 o f 7 × 7 × 7 ) ens.

Fibonacci getalle

0 ; 1 ; 1 ; 2 ; 3 ; 5 ; 8 ; 13 ; 21 ; 34 ; . . .

Die waarde van ʼn term in die reeks word gevind deur die vorige twee getalle in die reeks bymekaar te tel. Die 2 word gevind deur die vorige twee getalle in die reeks bymekaar te tel ( 1 + 1 ). Die 21 word gevind deur die twee getalle voor die 2 in die reeks bymekaar te tel ( 8 + 13 ). Die volgende getal in die reeks sal 55 wees ( 21 + 34 ).

Kan jy die volgende paar getalle vind?

Khan academy video oor getalpatrone - 1

Gestel jy en 3 vriende besluit om te studeer vir wiskunde, en dat julle om ʼn vierkantige tafel sit. ʼn Paar minute later sluit 2 ander vriende by julle aan en hulle wil kom sit. Om sitplek te kry vir hulle, besluit julle om ʼn tafel te skuif en dit langs julle tafel te sit sodat daar genoeg sitplek is vir die 6 van julle. Daarna besluit nog 2 van jou vriende om by julle aan te sluit en julle skuif ʼn derde tafel sodat daar genoeg plek is vir 8 van julle.

Twee ekstra mense kan sit vir elke tafel wat hulle bysit.

Ondersoek hoe die aantal mense om die tafels verband hou met die aantal tafels.

  1. Aantal tafels , n Aantal mense wat sitplek het
    1 4 = 4
    2 4 + 2 = 6
    3 4 + 2 + 2 = 8
    4 4 + 2 + 2 + 2 = 10
    n 4 + 2 + 2 + 2 + ... + 2
  2. Ons kan sien dat met 3 tafels is daar plek vir 8 mense, met 4 tafels is daar plek vir 10 mense ens. Ons begin met 4 mense en voeg elke keer 2 mense by. So, vir elke tafel wat bygevoeg word, is daar sitplek vir nog 2 mense.

Questions & Answers

what's a psy.d degree
Robin Reply
Psychology Doctorate. The main difference between PsyD and PhD Psychology is that PsyD mainly focuses on clinical sessions and PhD focuses on research.
Shrajan
so most of the phd holders become professors teaching what they have learnt
Bridget
Hi, I have a question. What factors influence social facilitation and social inhibition in groups?
Amritpal Reply
it really depends on that person on how the can task in life either they can work better with other people or you do worse working with people.
Lametra
the task
Lametra
they task
Lametra
Do you know of any studies done to show social facilitation and social inhibition
Amritpal
social facilitation is often influenced by the person's perception of the situation and their appraisal of the task. for example, a track athlete who views their competition as a challenge rather than a threat, will tend to run the fastest they have ever ran under a large crowd.
fady
Another condition is if the person has mastered the ability to perform that task. A track athlete who trains everyday, will perform above average under a large crowd, however, someone who does not run, will tend to do worse than their actual ability under a large crowd
fady
social inhibition can be explained through evolutionary biology or attachment personality theory. some people develop an avoidance personality trait, which when they feel under pressure, they tend to leave the group or avoid a gathering due to high lev of stress
fady
Does anyone know how I can transfer my higher national diploma credits in usa?
Qwanta Reply
Oh wow. I never realised there was a chat on this app!
Amritpal Reply
Then welcome dearest
Bridget
Thank you! ❤️
Amritpal
thank you
Ana
Hello Ana, good afternoon from here
Philip Reply
hello im new student here.
Junalyn Reply
o sorry madm
Rai
hello
Rai
I m also student.
Rai
hi
Kavya
what is easier option to psychology?
Dhanaraj
I'm new too
Deniz
As in the the specialisation or ?
Bridget
good morning
Ana
understanding human nature is what we are going to talk about.
Ana
okay, go ahead
Philip
“ Every child is left to evaluate his experiences for himself, and to take care of his own personal development outside the classroom. There is no tradition for the acquisition of a true knowledge of the human psyche. The science of human nature thus finds itself today in the position that chemis
Ana
well, I think every individual is different and to a great extent we can't say confidently that we understand the human nature in its entirety
Philip
lack determines what we will become in life?.
Ana
Not 100% but it plays a huge role
Philip
Hi! I wasn't aware there was a chat feature on this app 😊
Ophelia
👍Philip Anyaegbu
Ana
cool
Ana
👍
Ana
yes Ana I'm here
Philip
alternatively we are different, we have basic similar qualities
Bridget
Yes true Bridget.
Philip
hello there
Ciel
Hi
Philip
hi
Ej
hi
KUNDAN
hi
Ana
who we are how we think what we do insight
Ana
@ bridget. yes that's true
Ana
Ana ioanidis? do you speak Greek?
Qwanta
Qwanta no I dont speak Greek my husband does
Ana
are you a psychologist? or your husband?
Qwanta
I need some reliable informations about my studies...
Qwanta
not a psychologist
Ana
I ask questions
Ana
so what is the cause why a person experiences a psychological disorder if it not of their own?
Junalyn Reply
it's partly genetics,culture, environment and substance abuse. generally these are the common factors which can lead to most of the disorders
war
waoo
Rai
r u proficcer
Rai
u r psychology subject
Rai
not a professor but a clinical psychologist
war
can i ask you, i keep getting headache, and had a history of hypothyroid ans diagnosed as having mild anxiety disorder. i want to finish. my undergraduate psychology thesis.. but always unable to have good ambition and energy to focus on writing the case and the theories... whats the best remedy
Astaroxche
had a headache and have a history
Ana
297 according to the DSM 5
fady
how many disorders are there
Janareon Reply
interesting question
Mahmoud
it is😅
Nelly
I'm guessing it's in the tens of thousands, maybe hundreds if you include counter interactions and stuff like it. although I'm sure it's almost impossible to know for sure, unless you're very rich and connected to the right people. but as I said: guessing.
Beenie
There are more than 200 classified forms of mental illness. Some of the more common disorders are: clinical depression, bipolar disorder, dementia, schizophrenia and anxiety disorders. Symptoms may include changes in mood, personality, personal habits and/or social withdrawal. that is what I think
Mahmoud
too difficult to number. diagnosing a disorder is just checking off boxes on a compilation of symptoms that might match any particular condition on the DSM
what is psychology of the guest
Lirilong Reply
I don't understand the question can you elaborate?
Edgar
the study of philosophy gives to the sociologist
Aman Reply
why women are viewed as far more emotional than men?
Wario Reply
because they actually are ,I guess.
Collins
May be they are biologically milder than man. It does not mean they are not equal with man. Man can also be emotional and can are oppressed with traditional norms. For example, man are not to be cry, in actual man are also emotional being and they cannot have the right to show their sentiment.
shine
sollungal bro sollungal...
Balaji
because of she has hormonal fluctuations than men..
bavi
usually women are more emotional than men and they are multi talented people
lavanya
Both men and women are capable of expressing emotions. But women has the highest percentage of doing that. Because our society is conditioned by nature in such a way that men are expected to suppress their emotions and motivate them through their acts or thoughts, which has it's side effects of....
Santos
denial of any emotion which they feel that useless at that point. Women in the other hand were encouraged/not controlled to suppress their emotions and let them out what they feel about it. I feel that's the wonderful superpower of the women.
Santos
y
Mahmoud
Men's emotion comes mostly with memories triggered by senses. That means, they thoughts have the power to decide whether to let go of emotions or not.
Santos
Q
Mark
because women tend to be more agreeable than men.
Edgar
women at a young age are conditioned to be more in tune with emotion than man should be less
David
The question is "Why women Viewed are as far more emotional than men ?" it's not a question whether women are more emotional than men. This is more an issue about the point of view from the observer, his/her assumption what emotional behavior is or what emotional behavior is.
Mehmet
The anwers are answers more to the question " Are women more emotional than men?"
Mehmet
hi are you on what'sap
Wunuji Reply
no not really a fan of social laziness
Robert
huh
Parmizan
is there any way for a Btech E.C.E. graduate to take on MSC. PSYCHOLOGY
devesh
ya you can just by cracking entrance , if in India
Mansi
Any stream in UG can go for M.Sc (Psychology)
classification of traits and how they are measured
chinedu Reply
what was Freud's first name?
Robin Reply
Sigmund
Dentriodite
sigmund
Margie
Sigismund Schlomo Freud
Mohammad
Sigmund Freud
Talal
sigmund
Ankita
Leon Vygotsky and Sergei Rubenstein please tell me contributions of these personalities in in 4 lines
Uzma
sigmund Freud
Harpreet
Lev Vygotsky was the founder of socio-cultural theory
Jo
So psychology was based off of the Greek gods I that right or no?
Tanya Reply
psychology is the study. anything -ology is the study of a certain field. Psyche is a mortal woman who becomes divine in Greek mythology. The etymology of the word "psyche" in Greek means "spirit" or "soul"
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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