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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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