Hunter–Saxton equation: Difference between revisions
en>Citation bot 1 m [Pu381]Tweak: pages. Formatted dashes. |
en>Gisling |
||
Line 1: | Line 1: | ||
[[File:Spiral of Theodorus.svg|thumb|right|400px|The spiral of Theodorus up to the triangle with a hypotenuse of √17]] | |||
In [[geometry]], the '''spiral of Theodorus''' (also called ''square root spiral'', ''Einstein spiral'' or ''Pythagorean spiral'')<ref name=KAHN2>. Also, this was used to visualize certain things in nature | |||
{{cite arxiv | |||
|last=Hahn | |||
|first=Harry K. | |||
|title=The Ordered Distribution of Natural Numbers on the Square Root Spiral | |||
|eprint=0712.2184 | |||
}}</ref> is a [[spiral]] composed of [[contiguous]] [[right triangle]]s. It was first constructed by [[Theodorus of Cyrene]]. | |||
==Construction== | |||
The spiral is started with an [[isosceles]] right triangle, with each [[Cathetus|leg]] having unit [[length]]. Another right triangle is formed, an [[automedian triangle|automedian right triangle]] with one leg being the [[hypotenuse]] of the prior triangle (with length [[square root of 2|√2]]) and the other leg having length of 1; the length of the hypotenuse of this second triangle is [[square root of 3|√3]]. The process then repeats; the ''i''th triangle in the sequence is a right triangle with side lengths √''i'' and 1, and with hypotenuse {{sqrt|''i'' + 1}}. | |||
==History== | |||
Although all of Theodorus' work has been lost, [[Plato]] put Theodorus into his dialogue ''[[Theaetetus (dialogue)|Theaetetus]]'', which tells of his work. It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are [[Irrational number|irrational]] by means of the Spiral of Theodorus.<ref> | |||
{{citation | |||
|last=Nahin joe mo | |||
|first=Paul J. | |||
|title=An Imaginary Tale: The Story of [the Square Root of Minus One<nowiki>]</nowiki> | |||
|publisher=Princeton University Press | |||
|page=33 | |||
|url=http://books.google.com/?id=WvcfqBgZDWQC&printsec=frontcover | |||
|isbn=0-691-02795-1 | |||
|year=1998 | |||
}}</ref> | |||
Plato does not attribute the irrationality of the [[square root of 2]] to Theodorus, because it was well known before him. Theodorus and Theaetetus split the rational numbers and irrational numbers into different categories.<ref> | |||
{{citation | |||
|last=Plato | |||
|last2=Dyde | |||
|first2=Samuel Walters | |||
|title=The Theaetetus of Plato | |||
|publisher=J. Maclehose | |||
|pages=86–87. | |||
|url=http://books.google.com/?id=wt29k-Jz8pIC&printsec=titlepage | |||
|year=1899 | |||
}}</ref> | |||
==Hypotenuse== | |||
Each of the triangles' hypotenuses ''h<sub>i</sub>'' gives the [[square root]] of the corresponding [[natural number]], with ''h''<sub>1</sub> = √2. | |||
Plato, tutored by Theodorus, questioned why Theodorus stopped at √17. The reason is commonly believed to be that the √17 hypotenuse belongs to the last triangle that does not overlap the figure.<ref name=LONG> | |||
{{cite web | |||
|last=Long | |||
|first=Kate | |||
|title=A Lesson on The Root Spiral | |||
|url=http://courses.wcupa.edu/jkerriga/Lessons/A%20Lesson%20on%20Spirals.html | |||
|accessdate=2008-04-30 | |||
}}</ref> | |||
===Overlapping=== | |||
In 1958, Erich Teuffel proved that no two hypotenuses will ever coincide, regardless of how far the spiral is continued. Also, if the sides of unit length are extended into a [[line (geometry)|line]], they will never pass through any of the other vertices of the total figure.<ref>Erich Teuffel, Eine Eigenschaft der Quadratwurzelschnecke, ''Math.-Phys. Semesterber.'' 6 (1958), pp. 148-152.</ref><ref name=LONG/> | |||
==Extension== | |||
[[File:Colored extended spiral of roots.pdf|thumb|Colored extended spiral of Theodorus with 120 triangles]] | |||
Theodorus stopped his spiral at the triangle with a hypotenuse of √17. If the spiral is continued to infinitely many triangles, many more interesting characteristics are found. | |||
===Growth rate=== | |||
====Angle==== | |||
If φ<sub>''n''</sub> is the angle of the ''n''th triangle (or spiral segment), then: | |||
:<math>\tan\left(\varphi_n\right)=\frac{1}{\sqrt{n}}.</math> | |||
Therefore, the growth of the angle φ<sub>''n''</sub> of the next triangle ''n'' is:<ref name=KAHN2/> | |||
:<math>\varphi_n=\arctan\left(\frac{1}{\sqrt{n}}\right).</math> | |||
The sum of the angles of the first ''k'' triangles is called the total angle φ(''k'') for the ''k''th triangle, and it equals:<ref name=KAHN2/>{{Clarify|date=June 2012|reason=It's not clear what c_2(k) is; giving its limit at infinity is not enough}} | |||
:<math>\varphi\left (k\right)=\sum_{n=1}^k\varphi_n = 2\sqrt{k}+c_2(k)</math> | |||
with | |||
:<math>\lim_{k \to \infty} c_2(k)= - 2.157782996659\ldots.</math> | |||
[[File:Spiral of Theodorus triangle.svg|thumb|A triangle or section of spiral]] | |||
====Radius==== | |||
The growth of the radius of the spiral at a certain triangle ''n'' is | |||
:<math>\Delta r=\sqrt{n+1}-\sqrt{n}.</math> | |||
===Archimedean spiral=== | |||
The Spiral of Theodorus [[approximate]]s the [[Archimedean spiral]].<ref name=KAHN2/> Just as the distance between two windings of the Archimedean spiral equals [[mathematical constant]] [[pi]], as the number of spins of the spiral of Theodorus approaches [[infinity]], the distance between two consecutive windings quickly approaches π.<ref> | |||
{{cite arxiv | |||
|last=Hahn |first=Harry K. | |||
|year=2008 | |||
|title=The distribution of natural numbers divisible by 2, 3, 5, 7, 11, 13, and 17 on the Square Root Spiral | |||
|eprint=0801.4422 | |||
}}</ref> | |||
The following is a table showing the distance of two windings of the spiral approaching pi: | |||
{| class="wikitable" | |||
!Winding No.: | |||
!width=200px|Calculated average winding-distance | |||
!width=200px|Accuracy of average winding-distance in comparison to π | |||
|- | |||
|2 | |||
|3.1592037 | |||
|99.44255% | |||
|- | |||
|3 | |||
|3.1443455 | |||
|99.91245% | |||
|- | |||
|4 | |||
|3.14428 | |||
|99.91453% | |||
|- | |||
|5 | |||
|3.142395 | |||
|99.97447% | |||
|- | |||
|[[Limit of a function#Limits involving infinity|→]] ∞ | |||
|→ π | |||
|→ 100% | |||
|} | |||
As shown, after only the fifth winding, the distance is a 99.97% accurate approximation to π.<ref name=KAHN2/> | |||
==Continuous curve== | |||
The question of how to [[interpolation|interpolate]] the discrete points of the spiral of Theodorus by a smooth curve was proposed and answered in {{Harv|Davis|1993|loc = pp. 37–38 }} by analogy with Euler's formula for the [[gamma function]] as an [[Interpolation|interpolant]] for the [[factorial]] function. [[Philip J. Davis|Davis]] found the function | |||
:<math>T(x) = \prod_{k=1}^\infty \frac{1 + i/\sqrt{k}}{1 + i/\sqrt{x+k}} \qquad ( -1 < x < \infty )</math> | |||
which was further studied by his student [[Jeffery J. Leader|Leader]]<ref>[[Jeffery J. Leader|Leader, J.J.]] The Generalized Theodorus Iteration (dissertation), 1990, Brown University</ref> and by [[Arieh Iserles|Iserles]] (in an appendix to {{Harv|Davis|1993}} ). An axiomatic characterization of this function is given in {{Harv|Gronau|2004}} as the unique function that satisfies the [[functional equation]] | |||
:<math>f(x+1) = \left( 1 + \frac{i}{\sqrt{x+1} }\right) \cdot f(x),</math> | |||
the initial condition <math>f(0) = 1,</math> and [[Monotonic function|monotonicity]] in both [[Argument (complex analysis)|argument]] and [[Absolute value|modulus]]; alternative conditions and weakenings are also studied therein. An alternative derivation is given in {{Harv | Heuvers | Moak | Boursaw | 2000}}. | |||
Some have suggested a different interpolant which connects the spiral and an alternative inner spiral, as in {{Harv|Waldvogel|2009}}. | |||
==See also== | |||
*[[Fermat's spiral]] | |||
==References== | |||
{{reflist}} | |||
{{refbegin}} | |||
* {{Citation | title = Spirals from Theodorus to Chaos | first = P. J. | last = Davis | authorlink = Philip J. Davis |year = 1993 }} | |||
* {{Citation | doi = 10.2307/4145130 | title = The Spiral of Theodorus | first = Detlef| last = Gronau | journal = [[The American Mathematical Monthly]] | volume = 111 |date=March 2004 | pages = 230–237 | issue = 3 | publisher = Mathematical Association of America | jstor = 4145130 }} | |||
* {{Citation | first1 = J. | last1 = Heuvers | first2 = D. S. | last2 = Moak | first3 = B | last3 = Boursaw | chapter = The functional equation of the square root spiral | title = Functional Equations and Inequalities | editor = T. M. Rassias | year = 2000 | pages = 111–117 }} | |||
* {{Citation | title = Analytic Continuation of the Theodorus Spiral | first = Jörg | last = Waldvogel | year = 2009 | url = http://www.math.ethz.ch/~waldvoge/Papers/theopaper.pdf }} | |||
{{refend}} | |||
{{Greek mathematics}} | |||
[[Category:Spirals]] |
Revision as of 14:44, 11 January 2014
In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral)[1] is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene.
Construction
The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the ith triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse Template:Sqrt.
History
Although all of Theodorus' work has been lost, Plato put Theodorus into his dialogue Theaetetus, which tells of his work. It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are irrational by means of the Spiral of Theodorus.[2]
Plato does not attribute the irrationality of the square root of 2 to Theodorus, because it was well known before him. Theodorus and Theaetetus split the rational numbers and irrational numbers into different categories.[3]
Hypotenuse
Each of the triangles' hypotenuses hi gives the square root of the corresponding natural number, with h1 = √2.
Plato, tutored by Theodorus, questioned why Theodorus stopped at √17. The reason is commonly believed to be that the √17 hypotenuse belongs to the last triangle that does not overlap the figure.[4]
Overlapping
In 1958, Erich Teuffel proved that no two hypotenuses will ever coincide, regardless of how far the spiral is continued. Also, if the sides of unit length are extended into a line, they will never pass through any of the other vertices of the total figure.[5][4]
Extension
Theodorus stopped his spiral at the triangle with a hypotenuse of √17. If the spiral is continued to infinitely many triangles, many more interesting characteristics are found.
Growth rate
Angle
If φn is the angle of the nth triangle (or spiral segment), then:
Therefore, the growth of the angle φn of the next triangle n is:[1]
The sum of the angles of the first k triangles is called the total angle φ(k) for the kth triangle, and it equals:[1]Template:Clarify
with
Radius
The growth of the radius of the spiral at a certain triangle n is
Archimedean spiral
The Spiral of Theodorus approximates the Archimedean spiral.[1] Just as the distance between two windings of the Archimedean spiral equals mathematical constant pi, as the number of spins of the spiral of Theodorus approaches infinity, the distance between two consecutive windings quickly approaches π.[6]
The following is a table showing the distance of two windings of the spiral approaching pi:
Winding No.: | Calculated average winding-distance | Accuracy of average winding-distance in comparison to π |
---|---|---|
2 | 3.1592037 | 99.44255% |
3 | 3.1443455 | 99.91245% |
4 | 3.14428 | 99.91453% |
5 | 3.142395 | 99.97447% |
→ ∞ | → π | → 100% |
As shown, after only the fifth winding, the distance is a 99.97% accurate approximation to π.[1]
Continuous curve
The question of how to interpolate the discrete points of the spiral of Theodorus by a smooth curve was proposed and answered in Template:Harv by analogy with Euler's formula for the gamma function as an interpolant for the factorial function. Davis found the function
which was further studied by his student Leader[7] and by Iserles (in an appendix to Template:Harv ). An axiomatic characterization of this function is given in Template:Harv as the unique function that satisfies the functional equation
the initial condition and monotonicity in both argument and modulus; alternative conditions and weakenings are also studied therein. An alternative derivation is given in Template:Harv.
Some have suggested a different interpolant which connects the spiral and an alternative inner spiral, as in Template:Harv.
See also
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Template:Refbegin
- Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
- ↑ 1.0 1.1 1.2 1.3 1.4 . Also, this was used to visualize certain things in nature Template:Cite arxiv
- ↑
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - ↑
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - ↑ 4.0 4.1 Template:Cite web
- ↑ Erich Teuffel, Eine Eigenschaft der Quadratwurzelschnecke, Math.-Phys. Semesterber. 6 (1958), pp. 148-152.
- ↑ Template:Cite arxiv
- ↑ Leader, J.J. The Generalized Theodorus Iteration (dissertation), 1990, Brown University