Problem Statement:
A spiralateral is a sequence of line segments that form a spiral like shape. To draw one you simply choose a starting point, and draw a line the number of units that's first in your sequence. Always draw the first segment towards the top of your paper. Then make a clockwise 90 degree turn and draw a segment that is as long as the second number in your sequence. Continue to complete your sequence. Some spiralaterals end at their starting point where as others have no end, this will be further explained later in the write up. I explored the patterns created by length of the sequence used to create the spiralaterals. I also explored the difference in the pattern when the numbers were in a different order.

Process:
Initially I believed that all spiralaterals ended at their starting point, but I later found out that this wasn't true. I also believed that the order of the sequence of numbers wouldn't change the shape but it would simply have it turned a different way.

For each of my exploration questions I simply drew spiralaterals that satisfied the question. For example one of my questions was "Does the number of numerals in the sequence change the pattern?" To test this I drew a three number spiralateral, a 4 sequence spiralateral and a 5 sequence spiralateral, I found out that the number of numbers actually does affect the pattern of the spiralateral. I had no problems trying to solve this POW.

I had no assistance in doing this POW.

Results and Conclusions:
As I drew the spiralaterals I found that spiralaterals with an even number of numbers in each sequence tended not to end at the starting point. I also discovered that if they had an even number of numerals in the sequence, but they repeated a number then it would end. All spiralaterals with an odd number of numerals will end where the started and continue to cycle around. If a spiralateral repeats a number then it must end; this applies to all sequences whether they be odd...

...SEQUENCE
* In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, asequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.
* For example, {M, A, R, Y} is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from {A, R, M, Y}. Also, the sequence {1, 1, 2, 3, 5, 8}, which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers {2, 4, 6,...}. Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence { } is included in most notions of sequence, but may be excluded depending on the context.
ARITHMETIC SEQUENCE
* A sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18 which has...

...In my research of the Fibonacci Numbers, I have found that the Fibonacci numbers appear anywhere from leafs on plants, patterns of flowers, in fruits, some animals, even in the human body. Could this be nature’s numbering system?
For those who are unfamiliar with the Fibonacci numbers they are a series of numbers discovered by Leonardo Fibonacci in the 12th century in an experiment with rabbits. The order goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and so on. Starting with 1, each new number is simply the sum of the two before it. The ratio, which is called the Golden Ratio, between the numbers is 1.618034
The most exciting thing about the Fibonacci numbers is how it is portrayed in the human body. For example, the Fibonacci numbers can be seen in the human hand. We have 1 thumb on each hand, 2 bones in each thumb, 3 bones in each finger, 5 digits on each hand, and 8 fingers. You will also find that you have 1 nose, 2 eyes, 3 segments in each limb and the 5 fingers on each hand. Not to mention the Golden Ratio being found in the proportions and measurements of the human body. The ratio between the forearm and the hand. The ratio of the distance between the navel and the knee. The ratio of distance between the knee and the end of the foot. These are just a few examples that I found to be very interesting.
Aside from the body,...

...The numbers are overwhelming: Over the next 17 years, 350 million rural residents (more than the entire U.S. population today) will leave the farm and move to China’s cities. That will bring the Chinese urban population from just under 600 million today to close to 1 billion, changing China into a country where more than two-thirds of its people are city dwellers, says Jonathan Woetzel, a director in McKinsey’s Shanghai office. The change will reverse China’s centuries-old identity as a largely rural country. Thirty years ago, when China started modernizing its economy, more than 80% of Chinese lived in the countryside. And just six years ago it still was about 60%. Today China is just under 50% urban.
The newly urbanized population will live in eight megacities, those with a population of more than 10 million, as well 15 big cities with populations between 5 million and 10 million. In addition, by 2025 China will probably have at least 221 cities with a population over 1 million, estimates Woetzel. That compares with 35 cities of that scale across all of Europe today. These new urbanites are expected to be a powerful booster of growth: Urban consumption as a share of gross domestic product will most likely rise from 25% today to roughly 33% by 2025. “Urbanization is the engine of the Chinese economy—it is what has driven productivity growth over the last 20 years,” says Woetzel. “And China has the potential to keep doing this for the next 20 years.”...

...sensitive earth fault
ANSI 50BF – Breaker failure
ANSI 46 -Negative sequence / unbalance
ANSI 49RMS – Thermal overload
CURRENT PROTECTION FUNCTIONS
ANSI 50/51 – PHASE OVERCURRENT
Three-phase protection against overloads and phase-to-phase short-circuits.
ANSI 50N/51N OR 50G/51G – EARTH FAULT
Earth fault protection based on measured or calculated residual current values:
ANSI 50N/51N: Residual current calculated or measured by 3 phase current sensors
ANSI 50G/51G: residual current measured directly by a specific sensor
ANSI 50BF – BREAKER FAILURE
If a breaker fails to be triggered by a tripping order, as detected by the non-extinction of the fault current, this backup protection sends a tripping order to the upstream or adjacent breakers.
ANSI 46 – NEGATIVE SEQUENCE / UNBALANCE
Protection against phase unbalance, detected by the measurement of negative sequence current:
Sensitive protection to detect 2-phase faults at the ends of long lines
Protection of equipment against temperature build-up, caused by an unbalanced power supply, phase inversion or loss of phase, and against phase current unbalance
ANSI 49RMS – THERMAL OVERLOAD
Protection against thermal damage caused by overloads on machines (transformers, motors or generators). The thermal capacity used is calculated according to a mathematical model which takes into account:
Current RMS values
Ambient temperature
Negative sequence current, a...

...Note: These are not sample questions, but questions that explore some of the concepts that
may be used. The intention is that you should get prepared with the concepts rather than just
focusing on a set of questions.
----------------------------------------------------------------------------------1. What are the total number of divisors of 600(including 1 and 600)?
a.
b.
c.
d.
24
40
16
20
2. What is the sum of the squares of the first 20 naturalnumbers (1 to 20)?
a.
b.
c.
d.
2870
2000
5650
44100
3. What is∑
items?
a.
b.
c.
d.
(
), where
is the number of ways of choosing k items from 28
) where
is the number of ways of choosing k items from 28
406 *
306 *
28 *
56 *
4. What is ∑
items?
(
a.
b.
c.
d.
5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names
(but she does not have any of the names). She needs to quickly contact Deepak Sharma to
convey a message to him. If each call takes 2 minutes to complete, and every call is
answered, what is the minimum amount of time in which she can guarantee to deliver the
message to Mr Sharma.
a.
b.
c.
d.
18 minutes
610 minutes
206 minutes
34 minutes
6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively.
What is the average time per call?
a.
b.
c.
d.
4 minutes
7 minutes
1 minutes
5 minutes...

...The Construction Sequence
Although the specific sequence of construction steps varies and overlaps, generally we build your home in the following order:
▪ Survey
▪ Permits
▪ Sewer & Water
▪ Plan Commission
▪ Building Department
▪ Foundation
▪ Excavation
▪ Footer
▪ Form and pour walls
▪ Perimeter drain
▪ Waterproof
▪ Ground rough plumbing
▪ Basement/Crawl space floors
▪ Garage Floor
▪ Back Fill
▪ Utilities
▪ Framing
▪ Roofing
▪ Rough-in of mechanical systems
▪ Fireplace
▪ HVAC (heating, fireplace ventilating, and air conditioning)
▪ Plumbing
▪ Electrical (extra outlets need to be installed at this point)
▪ Cable and phone outlets
▪ Rough inspections
▪ Insulation
▪ Siding
▪ Stone or brick, if applicable
▪ Deck, if applicable
▪ Drywall
▪ Prime Walls (Paint Walls if using pre-stained trim) & Paint Ceilings
▪ Hardwood floors
▪ Interior trim
▪ Cabinets
▪ Doors
▪ Baseboards, casings, other details
▪ Finish work
▪ Countertops
▪ Tile
▪ Vinyl
▪ Sand and coat hardwood floors
▪ Paint Finish Work and Stain...

...Sequence Essay
In a sequence essay, you are writing to describe a series of events or a process in some sort of order. Usually, this order is based on time. You organize the essay by writing about each step of the process in the order it occurred.
Example question: | Write an essay outlining the stages of the salmon life cycle. |
Introduction: | Describe what a salmon is like. |
Supporting paragraphs: | 1. Describe young salmon. |
| 2. Describe adult salmon. |
| 3. Describe what salmon do before they die. |
Summary paragraph: | Summarize the main steps of the salmon life cycle. |
Sequence Essay Example
Life Cycle of Tulips
The life cycle of tulips start when the bulbs are planted from mid-September to mid-November and ends when the leaves fade and eventually wither away. The cup-shaped flowers are beautiful to look at and have an ability to make a glum person cheerful. This article gives an insight into the life cycle of tulips.
Tulips were considered to be the flowers of God due to their beauty and perfection, by the Turks. Many of us believe tulips are native of Holland. Contrary to the belief, there is not a single species of tulip native to Holland. Tulips belong to Central and Western Asia and it were the nomadic tribes who brought the tulips to Turkey. Turkey was called the Ottoman Empire in olden days. It were the Turks who popularized this beautiful spring flower, tulip. In the late 16th...

...Sequences and Convergence
Let x1 , x2 , ..., xn , ... denote an infinite sequence of elements of a metric space
(S, d). We use {xn }∞
n=1 (or simply {xn }) to denote such a sequence.
Definition 1 Consider x0 ∈ S. We say that the sequence {xn } converges to x0
when n tends to infinity iff: For all > 0, there exists N ∈ N such that for all
n > N , d(xn , x0 ) <
We denote this convergence by lim xn = x0 or simply xn −→ x0 .
n→∞
Example 2 Consider the sequence {xn } in R, defined by xn = n1 . Then xn −→
0.
The way to prove this is standard: fix > 0. We need to find N ∈ N such that
for all n > N , d(xn , 0) < . We have d(xn , 0) = |xn − 0| = | n1 |
So it is enough that n1 < , or equivalently n > 1 . So choosing N > 1 we know
that for all n > N , d(xn , 0) < .
The fact that we define the concept of convergence does not imply that every
sequence converges. This is illustrated in the next two examples. Let’s begin
with a remark about what it means for a sequence {xn } not to converge to x0 .
Remark: To know what the non-convergence of a sequence means, we need
to write the negation of the definition of convergence. That reduces to: There
exists > 0, such that for all N ∈ N, there exists n > N such that d(xn , x0 ) ≥ .
For the ones of you familiar with propositional logic, notice that convergence to
x0 can be written as
(∀ > 0)(∃N ∈ N)(∀n > N )d(xn , x0 ) <
Its negation...

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":33121054,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":2,"pageRange":"1-2","totalPages":2}},"access":"premium","title":"Number and Sequence","additionalIds":[9,103],"additional":["Entertainment","Entertainment\/Film"],"loadedPages":{"html":[],"text":[1,2]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Number-And-Sequence-122392.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.9","language":"en_US"}}