**Gist**

an unforeseen combination of circumstances or the resulting state that calls for immediate action.

2. an urgent need for assistance or relief.

**Details**

An emergency is an urgent, unexpected, and usually dangerous situation that poses an immediate risk to health, life, property, or environment and requires immediate action. Most emergencies require urgent intervention to prevent a worsening of the situation, although in some situations, mitigation may not be possible and agencies may only be able to offer palliative care for the aftermath.

While some emergencies are self-evident (such as a natural disaster that threatens many lives), many smaller incidents require that an observer (or affected party) decide whether it qualifies as an emergency. The precise definition of an emergency, the agencies involved and the procedures used, vary by jurisdiction, and this is usually set by the government, whose agencies (emergency services) are responsible for emergency planning and management.

**Defining an emergency**

An incident, to be an emergency, conforms to one or more of the following, if it:

* Poses an immediate threat to life, health, property, or environment

* Has already caused loss of life, health detriments, property damage, or environmental damage

* has a high probability of escalating to cause immediate danger to life, health, property, or environment

In the United States, most states mandate that a notice be printed in each telephone book that requires that someone must relinquish use of a phone line, if a person requests the use of a telephone line (such as a party line) to report an emergency. State statutes typically define an emergency as, "...a condition where life, health, or property is in jeopardy, and the prompt summoning of aid is essential."

Whilst most emergency services agree on protecting human health, life and property, the environmental impacts are not considered sufficiently important by some agencies. This also extends to areas such as animal welfare, where some emergency organizations cover this element through the "property" definition, where animals owned by a person are threatened (although this does not cover wild animals). This means that some agencies do not mount an "emergency" response where it endangers wild animals or environment, though others respond to such incidents (such as oil spills at sea that threaten marine life). The attitude of the agencies involved is likely to reflect the predominant opinion of the government of the area.

**Types of emergency**:

**Dangers to life**

Many emergencies cause an immediate danger to the life of people involved. This can range from emergencies affecting a single person, such as the entire range of medical emergencies including heart attacks, strokes, cardiac arrest and trauma, to incidents that affect large numbers of people such as natural disasters including tornadoes, hurricanes, floods, earthquakes, mudslides and outbreaks of diseases such as coronavirus, cholera, Ebola, and malaria.

Most agencies consider these the highest priority emergency, which follows the general school of thought that nothing is more important than human life.

**Dangers to health**

Some emergencies are not necessarily immediately threatening to life, but might have serious implications for the continued health and well-being of a person or persons (though a health emergency can subsequently escalate to life-threatening).

The causes of a health emergency are often very similar to the causes of an emergency threatening to life, which includes medical emergencies and natural disasters, although the range of incidents that can be categorized here is far greater than those that cause a danger to life (such as broken limbs, which do not usually cause death, but immediate intervention is required if the person is to recover properly). Many life emergencies, such as cardiac arrest, are also health emergencies.

**Dangers to the environment**

Some emergencies do not immediately endanger life, health or property, but do affect the natural environment and creatures living within it. Not all agencies consider this a genuine emergency, but it can have far-reaching effects on animals and the long term condition of the land. Examples would include forest fires and marine oil spills.

**Systems of classifying emergencies**

Agencies across the world have different systems for classifying incidents, but all of them serve to help them allocate finite resource, by prioritising between different emergencies.

The first stage of any classification is likely to define whether the incident qualifies as an emergency, and consequently if it warrants an emergency response. Some agencies may still respond to non-emergency calls, depending on their remit and availability of resource. An example of this would be a fire department responding to help retrieve a cat from a tree, where no life, health or property is immediately at risk.

Following this, many agencies assign a sub-classification to the emergency, prioritising incidents that have the most potential for risk to life, health or property (in that order). For instance, many ambulance services use a system called the Advanced Medical Priority Dispatch System (AMPDS) or a similar solution. The AMPDS categorises all calls to the ambulance service using it as either 'A' category (immediately life-threatening), 'B' Category (immediately health threatening) or 'C' category (non-emergency call that still requires a response). Some services have a fourth category, where they believe that no response is required after clinical questions are asked.

Another system for prioritizing medical calls is known as Emergency Medical Dispatch (EMD). Jurisdictions that use EMD typically assign a code of "alpha" (low priority), "bravo" (medium priority), "charlie" (requiring advanced life support), delta (high priority, requiring advanced life support) or "echo" (maximum possible priority, e.g., witnessed cardiac arrests) to each inbound request for service; these codes are then used to determine the appropriate level of response.

Other systems (especially as regards major incidents) use objective measures to direct resource. Two such systems are SAD CHALET and ETHANE, which are both mnemonics to help emergency services staff classify incidents, and direct resource. Each of these acronyms helps ascertain the number of casualties (usually including the number of dead and number of non-injured people involved), how the incident has occurred, and what emergency services are required.

**Agencies involved in dealing with emergencies**

Most developed countries have a number of emergency services operating within them, whose purpose is to provide assistance in dealing with any emergency. They are often government operated, paid for from tax revenue as a public service, but in some cases, they may be private companies, responding to emergencies in return for payment, or they may be voluntary organisations, providing the assistance from funds raised from donations.

Most developed countries operate three core emergency services:

Police – handle mainly crime-related emergencies.

Fire – handle fire-related emergencies and usually possess secondary rescue duties.

Medical – handle medical-related emergencies.

There may also be a number of specialized emergency services, which may be a part of one of the core agencies, or may be separate entities who assist the main agencies. This can include services, such as bomb disposal, search and rescue, and hazardous material operations.

The Military and the Amateur Radio Emergency Service (ARES) or Radio Amateur Civil Emergency Service (RACES) help in large emergencies such as a disaster or major civil unrest.

**Summoning emergency services**

Most countries have an emergency telephone number, also known as the universal emergency number, which can be used to summon the emergency services to any incident. This number varies from country to country (and in some cases by region within a country), but in most cases, they are in a short number format, such as 911 (United States and many parts of Canada), 999 (United Kingdom), 112 (Europe) and 000 (Australia).

The majority of mobile phones also dial the emergency services, even if the phone keyboard is locked, or if the phone has an expired or missing SIM card, although the provision of this service varies by country and network.

**Civil emergency services**

In addition to those services provided specifically for emergencies, there may be a number of agencies who provide an emergency service as an incidental part of their normal 'day job' provision. This can include public utility workers, such as in provision of electricity or gas, who may be required to respond quickly, as both utilities have a large potential to cause danger to life, health and property if there is an infrastructure failure.

**Domestic emergency services**

Generally perceived as pay per use emergency services, domestic emergency services are small, medium or large businesses who tend to emergencies within the boundaries of licensing or capabilities. These tend to consist of emergencies where health or property is perceived to be at risk but may not qualify for official emergency response. Domestic emergency services are in principal similar to civil emergency services where public or private utility workers will perform corrective repairs to essential services and avail their service at all times; however, these are at a cost for the service. An example would be an emergency plumber

**Emergency action principles (EAP)**

Emergency action principles are key 'rules' that guide the actions of rescuers and potential rescuers. Because of the inherent nature of emergencies, no two are likely to be the same, so emergency action principles help to guide rescuers at incidents, by sticking to some basic tenets.

The adherence to (and contents of) the principles by would-be rescuers varies widely based on the training the people involved in emergency have received, the support available from emergency services (and the time it takes to arrive) and the emergency itself.

**Key emergency principle**

The key principle taught in almost all systems is that the rescuer, whether a lay person or a professional, should assess the situation for danger.

The reason that an assessment for danger is given such high priority is that it is core to emergency management that rescuers do not become secondary victims of any incident, as this creates a further emergency that must be dealt with.

A typical assessment for danger would involve observation of the surroundings, starting with the cause of the accident (e.g. a falling object) and expanding outwards to include any situational hazards (e.g. fast moving traffic) and history or secondary information given by witnesses, bystanders or the emergency services (e.g. an attacker still waiting nearby).

Once a primary danger assessment has been complete, this should not end the system of checking for danger, but should inform all other parts of the process.

If at any time the risk from any hazard poses a significant danger (as a factor of likelihood and seriousness) to the rescuer, they should consider whether they should approach the scene (or leave the scene if appropriate).

**Managing an emergency**

There are many emergency services protocols that apply in an emergency, which usually start with planning before an emergency occurs. One commonly used system for demonstrating the phases is shown here on the right.

The planning phase starts at preparedness, where the agencies decide how to respond to a given incident or set of circumstances. This should ideally include lines of command and control, and division of activities between agencies. This avoids potentially negative situations such as three separate agencies all starting an official emergency shelter for victims of a disaster.

Following an emergency occurring, the agencies then move to a response phase, where they execute their plans, and may end up improvising some areas of their response (due to gaps in the planning phase, which are inevitable due to the individual nature of most incidents).

Agencies may then be involved in recovery following the incident, where they assist in the clear up from the incident, or help the people involved overcome their mental trauma.

The final phase in the circle is mitigation, which involves taking steps to ensure no re-occurrence is possible, or putting additional plans in place to ensure less damage is done. This should feed back into the preparedness stage, with updated plans in place to deal with future emergencies, thus completing the circle.

**State of emergency**

In the event of a major incident, such as civil unrest or a major disaster, many governments maintain the right to declare a state of emergency, which gives them extensive powers over the daily lives of their citizens, and may include temporary curtailment on certain civil rights, including the right to trial. For instance to discourage looting of an evacuated area, a shoot on sight policy, however unlikely to occur, may be publicized.

**Additional Information**

Emergency medicine is a medical specialty emphasizing the immediacy of treatment of acutely ill or injured individuals.

Among the factors that influenced the growth of emergency medicine was the increasing specialization in other areas of medicine. With the shift away from general practice—especially in urban centres—the emergency room became for many, in effect, a primary source of health care. Another factor was the adoption of a number of standard emergency procedures—such as immediate paramedic attention to severe wounds and the rapid transportation of the ill or injured to a hospital—that had evolved in the military medical corps; as used in the civilian hospital, these techniques resulted in such measures as the training of paramedics and the development of the hospital emergency room as a major trauma centre.

Together these factors led to a greatly increased demand for emergency services and in the early 1960s led to the full-time staffing of hospital emergency rooms. The physicians who led the emergency-room team, once recruited from other specialties, felt an increasing demand for training in the management of both major traumas and a wide range of acute medical problems. Emergency medicine became an officially recognized specialty in 1979. In the following decades, prehospital care benefited from technological advances, particularly in the area of cardiac life-support.

]]>

One way of stating the approximation involves the logarithm of the factorial:

where the big O notation means that, for all sufficiently large values of n, the difference between

and

will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent formThe error term in either base can be expressed more precisely as

corresponding to an approximate formula for the factorial itself,

Here the sign

, rather than only asymptotically:]]>

Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not widely available. Instead, tables of base-10 logarithms were used in science, engineering and navigation—when calculations required greater accuracy than could be achieved with a slide rule. By turning multiplication and division to addition and subtraction, use of logarithms avoided laborious and error-prone paper-and-pencil multiplications and divisions. Because logarithms were so useful, tables of base-10 logarithms were given in appendices of many textbooks. Mathematical and navigation handbooks included tables of the logarithms of trigonometric functions as well. For the history of such tables, see log table.

]]>For finite y,it is computable by brute force.It is monotonic with respect to y(if x>y,βB(n,x)>βB(n,y))

Define Bβ(x) as the smallest y which βB(x,y)=BB(x).It is finite for finite x.(because βB is monotonic,and has to start at 0 and get to BB(x) at infinity,and it can't change from BB(x)-1 to BB(x) at infinity-1(because you can't have infinity-1))It is uncomputable too,since by computing it we can find a non finite upper bound of βB,to replace the uncomputableness of βB(x,inf)

So yeah,two new interesting functions,of one is uncomputable(i found those functions when trying to induce a contradiction in BB(x)(using brute force,but forgot that the tape is infinite,thus proving that βB is computable at finite y)

Where should I submit them?Were them discovered before by other people?

What should they be called?(i called the βB function the busy little beaver function and the Bβ function the unbusy beaver function)

In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948.

In the same year, Casimir together with Dirk Polder described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface which is referred to as the Casimir–Polder force. Their result is a generalization of the London–van der Waals force and includes retardation due to the finite speed of light. Since the fundamental principles leading to the London–van der Waals force, the Casimir and the Casimir–Polder force, respectively, can be formulated on the same footing, the distinction in nomenclature nowadays serves a historical purpose mostly and usually refers to the different physical setups.

It was not until 1997 that a direct experiment by S. Lamoreaux quantitatively measured the Casimir force to within 5% of the value predicted by the theory.

The Casimir effect can be understood by the idea that the presence of macroscopic material interfaces, such as conducting metals and dielectrics, alters the vacuum expectation value of the energy of the second-quantized electromagnetic field. Since the value of this energy depends on the shapes and positions of the materials, the Casimir effect manifests itself as a force between such objects.

Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in turbulent water or gas illustrate the Casimir force.

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics it is significant in some aspects of emerging microtechnologies and nanotechnologies.

**Physical properties**

The typical example is of two uncharged conductive plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the quantum electrodynamic vacuum, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force – either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization.

The treatment of boundary conditions in these calculations has led to some controversy. In fact, "Casimir's original goal was to compute the van der Waals force between polarizable molecules" of the conductive plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.

Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm – about 100 times the typical size of an atom – the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).

]]>[6,28,496,8128,33550336,8589869056, 137438691328, 2305843008139952128].includes(x)

The longs can't outrun you]]>

a is about -0.23557

the average error is 0.003388

this can be used for stuff like fast inverse fourth root or something(ln(1+x) is used on the mantissa from 0 to 1)]]>

Assume we have an infinite grid of stars spaced evenly and we are not in one of them

The brightness (and tidal forces) we get is ∑∑∑1/((i-1/2)^2+(j-1/2)^2+(k-1/2)^2)

The question is,does this converge?

If we slightly tweak our model a bit,so that the universe on a polar coordinate,and the stars form a circular pattern,and the nth layer has n stars on it,we get an harmonic series of light which is unending and still less than the 3d universe.

Call Hubble to the rescue!

]]>There is a whole group of such systems of equations.

Such a system is solved as standard. First, we write down the parametrization of one equation.

And then we find the parameterization for the necessary parameters.

]]>Here is a relevant link: Double Factorial.

]]>j^2=1

so k^2=0

e^kx=cosk x+ksink x

e^kx=1+kx+0x/2+0k^2/6...=1+kx

cosk x=1

sink x=x

so tank x=x asink x=x Acosk x=1 acosk x=anything atank x=x

e^ix is on the x^2+y^2=1

e^jx is on the x^2-y^2=1

so e^kx is on the x^2+0y^2=1 or x=+-1

e^ix x is half the area of a sector

e^jx x is half the area of a hyperbola sector thingy

then e^kx x is half the area of a triangle(does work with cosk and sink)

conclusion:the zero factor crumples stuff up a lot]]>

|x/a|^n+|y/b|^n=1 where n>=2

<=>

|y/b|^n=1-|x/a|^n

<=>

y/b=+/- (1-|x/a|^n)^(1/n)

<=>

y=+/- b*(1-|x/a|^n)^(1/n) // absolute makes x<0 usable

a=semi-mayor axis (half-axis in x-direction)

b=semi-minor axis (half-axis in y-direction)

Of course, it has something of the hyperbola.

n=2 leaves the ellipse.

With n increasing from there, the shape converges to a rectangle.

The curvature is 0, where it crosses the axes.

Simplifying it to the supercircle,

which probably is an unsqueezed superelipse, so a=b:

On Wikipedia, they call a supercircle where n=4 a squircle.

Without shifting and variables kept, they give x⁴+y⁴=a⁴ <=> y=+/- (a⁴-x⁴)^(1/4).

With n instead of 4, its the equivalent of a=b in the superelipse-formula at the top.

It seems also to work with a z-part: **x^n+y^n+z^n=a^n <=> y=+/- (a^n-x^n-z^n)^(1/n)**

Basically I refer to the 2D-Case where z=0, but will expand to 3D at times.

f(x,z,a,n) = (a^n-x^n-z^n)^(1/n)

f'(x,z,a,n) = -x^(n-1)*(a^n-x^n-z^n)^(1/n-1) // slope

f''(x,z,a,n) = -(n-1)*x^(n-2)*(a^n-z^n)*(a^n-x^n-z^n)^(1/n-2) // curvature use for elbowradius

some limit cases:

for n=2 the sqircle is a circle

for n=1 the sqircle is a square

for 0 < n < 1 the sqircle is a star

domain of squircle funtion f(x,z,a,n): // xstart for slope-x-value newton aproxximation (functiondrawing)

a^n-x^n-z^n // content of the root

a^n-z^n-x^n>=0 // which shouldn't be 0 or negative

a^n-z^n>=x^n

x<=(a^n-z^n)^(1/n)

Calculating the area and the perimeter is said to be complicated.

Regarding the area, there is however a shortcut using the Lemniscate Constant L~2.62205755429211981 .

So the area is **A=L*sqrt(2)*a^2** . For now I will go with that.

A sidenote before I go deeper into the math:

While browsing the web I stumbled upon a post about a spherefactor-approach.

Below I mainly try to get the n out of the squircle functon.

Instead I throw in more common values out of the hyperbola properties.

c in f(x,a,c) is a counterpart for the semi major axis of a hyperbola

(how far the curve is pulled into an rectangular edge).

r in f(x,a,r) is the radius in the elbow of a hyperbola

(where the highest curvature is).

For the later an n which is described by r and a=r_min,

would probably have to be approximated.

I tried it with the newton procedure, which covered many cases.

The properties I come by may also be interresting for them selves

or handy for other calculations.

For getting the maximum radius (origin to rounded edge)

I'm intersecting the squircle with a line of slope=1:

f(x,a,n)=f(x,z=0,a,n)=(a^n-x^n)^(1/n) // n=4: **black** line in the graph

g(x)=x // straight 45° ascending line through origin

f(x)=g(x)

solve((a^n - x^n)^(1/n)=x,x)

The computer has not wanted to solve it with n,

but when I tried it with different numbers for n, it took the nth root,

so I've put n there.

x=a/2^(1/n) // simplest positive non-imaginary solution out of 5, n=4: **brown** line in the graph

y=x since symmetry

a:=r_min // **red** distance in the graph

d:=r_max // **blue** distance in the graph

r_max=a/2^(1/n)*sqrt(2)=**2^(1/2-1/n)*a**

diagonal=r_min*sqrt(2) // **blue** plus **green** line in the graph

c:=diagonal-r_max // **green** line in the graph

c=a*sqrt(2)-a/2^(1/n)*sqrt(2)

=(a-a/2^(1/n))*sqrt(2)=**sqrt(2)*(1-2^(-1/n))*a**

<=>

a=(2^(1/n-1/2)*c)/(2^(1/n)-1) and 2^(1/n)!=1

<=>

n=-(i*log(2))/(2*π*c_1-i*log((sqrt(2)*a)/(sqrt(2)*a-c)))

and sqrt(2) a!=c and a!=0 and log((sqrt(2)*a)/(sqrt(2)*a-c))+2*i*π*c_1!=0 and c_1 element Z

=log(4)/(2*log(a/(sqrt(2)*a-c))+4*i*π*c_1+log(2)) // variables real

Again without imaginaries:

c=sqrt(2)*(1-2^(-1/n))*a |/sqrt(2)*a

<=>

c/(sqrt(2)*a)=1-2^(-1/n) |-1

<=>

(c/(sqrt(2)*a))-1=-2^(-1/n) |*(-1)

<=>

2^(-1/n)=1-(2^(-1/2)*c/a) |^(-1)

<=>

2^(1/n)=1/(1-(2^(-1/2)*c/a)) |log, 1/(1-(2^(-1/2)*c/a))=(sqrt(2)*a)/(sqrt(2)*a-c)

<=>

1/n=log((sqrt(2)*a)/(sqrt(2)*a-c))/log(2) |^(-1)

<=>

n=log(2)/log((sqrt(2)*a)/(sqrt(2)*a-c))

c'=d/dn=-(a*2^(1/2-1/n)*log(2))/n^2 // for newton approximation

f(x,c,n)=(((2^(1/n-1/2)*c)/(2^(1/n)-1))^n-x^n)^(1/n)

=(2^(1-n/2)*((2^(1/n)-1)/c)^(-n)-x^n)^(1/n) // variables positive

f(x,a,c)=(a^(-(2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)))-x^(-(2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2))))^(log(a/(sqrt(2)*a-c))/log(2)+(2*i*π*c_1)/log(2))*sqrt(a^(-(2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)))*x^(-(2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)))*(x^((2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)))-a^((2*i*log(2))/(-2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)))))

and -2*i*log(a/(sqrt(2)*a-c))+4*π*c_1-i*log(2)!=0

Without imaginaries:

f(x,a,c)=(a^log(2)/log((sqrt(2)*a)/(sqrt(2)*a-c))-x^log(2)/log((sqrt(2)*a)/(sqrt(2)*a-c)))^(1/log(2)/log((sqrt(2)*a)/(sqrt(2)*a-c)))

=**((a^log(2)-x^log(2))/log(c/(sqrt(2)*a-c)+1))^(1/(log(2)*log(c/(sqrt(2)*a-c)+1)))** // variables positive

*Check:f(x,c,n)=0 // x-intersect=r_min(2^(1-n/2)*((2^(1/n)-1)/c)^(-n)-x^n)^(1/n)=0x=(2^(1-n/2)*((2^(1/n)-1)/c)^(-n))^(1/n) =(2^(1/n-1/2)*c)/(2^(1/n)-1) and 2^(1/n)!=1 // variables positive =r_min=a (see above)*

Elbow-radius:

r=1/curvature

r=1/f''(a/2^(1/n))

=-(a^(-n)*(a*2^(-1/n))^(2-n)*(a^n-(a*2^(-1/n))^n)^(2-1/n))/(n-1)

=(2^(-1-1/n)*a)/(1-n) // variables positive

For n between ]1,infinity[, this gives half the negative radius.*Why half and why negative ?*

Correction by manipulating the numerator (1 -> -2):

r=-2/f''(a/2^(1/n))

=-2*(2^(-1-1/n)*a)/(1-n)

=(2^(-1/n)*a)/(n-1)

<=>

a=2^(1/n)*(n-1)*r and Re(n)<1

<=>

a/r=2^(1/n)*(n-1)

<=>

n=not solvable

r'=d/dn=-(a*2^(-1/n)*(n^2-n*log(2)+log(2)))/((n-1)^2*n^2) // for newton approximation

f(x,r,n)=((2^(1/n)*(n-1)*r)^n-x^n)^(1/n)

=(2*(n-1)^n*r^n-x^n)^(1/n) // variables positive

f(x,a,r)=not findable

*f(x,r,n)=0 // x-intersect=r_min((2^(1/n)*(n-1)*r)^n-x^n)^(1/n)=0x=((2^(1/n)*(n-1)*r)^n)^(1/n) =2^(1/n)*n*r-2^(1/n)*r=2^(1/n)*(n-1)*r // variables positive =r_min=a (see above)*

checking it with some limit cases:

for n=2 the sqircle is a circle

r=(2^(-1/n)*a)/(n-1)

r=(2^(-1/2)*a)/(2-1)=a/sqrt(2)

<=>

a=sqrt(2)*r // shouldn't a=r ?

what would that further mean ?:

if r > a/sqrt(2) then its edgy

if r = a/sqrt(2) then its a circle

if r < a/sqrt(2) then its a squirce

for n=1 the sqircle is a square

r=(2^(-1/n)*a)/(n-1)

r=(2^(-1/1)*a)/(1-1)=division by zero, complex infinity

this result seems to be satisfying,

cause a square does have no radius.

for 0 < n < 1 the sqircle is a star

]]>After everything below I hold the opinion, that it is an asymmetric ellipse.

First I digged into Wikipedia.

The cause of the shape of eggs according to an article, linked there, about Mary Caswell Stoddard and her team:

"It begins when an unfertilized egg cell is added to a globule of yolk, and sent down a bird’s oviduct... ...On its travels, it is fertilized by sperm, surrounded by white, and coated in two membranes. The membranes are pumped with fluid like a balloon being inflated, and finally surrounded by a shell. Counter-intuitively, it’s not the shell that matters most, but the membranes. If you dissolve the shell in acid, the naked egg will still retain its original shape."

They took the Baker-Formula and matched bird eggs with it (EggxTractor).

There are different construction methods.

The Wikipedia article also links a paper titled the mathematics of egg shape of Yutaka Nishiyama.

After explaining the Descartes approach, he goes on with the Cassini approach, which is more or less a shortcut of the former.

This could probably be read before taking on the Baker-Formula:

y=t(1+a)^(1/1+a)*(1−a)^(a/1+a)

t=(equatorial diameter)^(-1) ?

a=ln(heightright)/ln(heightleft)

There is another equation which

I struggle to let go of just yet.

It's the Blaschke one, I found on mathtinkering:

x^1.5-l^0.5x+y^2=0

y = ± (sqrt(x)*sqrt(sqrt(a)-sqrt(x)))

Since 2021 this formula of Narushin (see there for variable descriptions) was hyped:

It already has this breadth value,

whch would have been left for me to calculate with the Baker formula

I will see how I like it.

So much for now.

I came across a link here.

In the relevant topic.

Interesting!

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