For shapes with curved boundary, calculus is usually required to compute the area.

For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.

For example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically ( or thermally ) insulated ; an insulated wall approximates an adiabatic boundary.

For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">

For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">

* Antiphase boundaries occur in ordered alloys: in this case, the crystallographic direction remains the same, but each side of the boundary has an opposite phase: For example, if the ordering is usually ABABABAB, an antiphase boundary takes the form of ABABBABA.

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.

For Abdur Rahman, delineating the boundary with India ( through the Pashtun area ) was far more significant, and it was during his reign that the Durand Line was drawn.

For younger stages, a Global Boundary Stratotype Section and Point ( GSSP ), a physical outcrop clearly demonstrates the boundary.

For case # 3, the two boundary pixels define a path which, if we painted the current pixel, may block us from ever getting back to the other side of the path.

For many reasons scholars today believe otherwise — for example, the gospel is based on Mark, and " it seems unlikely that an eyewitness of Jesus's ministry, such as Matthew, would need to rely on others for information about it "— and believe instead that it was written between about 80 – 90 AD by a highly educated Jew ( an " Israelite ", in the language of the gospel itself ), intimately familiar with the technical aspects of Jewish law, standing on the boundary between traditional and non-traditional Jewish values.

For example, the boundary between the Cretaceous period and the Paleogene period is defined by the Cretaceous – Paleogene extinction event, which marked the demise of the dinosaurs and many other groups of life.

( For comparison, a sphere is an orientable surface with no boundary.

For example, the Klein bottle has no boundary, where the surface stops abruptly, and it is non-orientable, as reflected in the one-sidedness of the immersion.

For instance, light that accidentally crosses a property boundary and annoys a neighbor is generally wasted and pollutive light.

For planetary science, the magnetopause is the boundary between the planet ’ s magnetic field and the solar wind.

For example, the discovery by Luis Alvarez and Walter Alvarez of an iridium-rich layer at the Cretaceous – Tertiary boundary made asteroid impact and volcanism the most favored explanations for the Cretaceous – Paleogene extinction event.

For the Panathenaic festival, arguably the most important civic festival at Athens, a torch race began at the altar, which was located outside the sacred boundary of the city, and passed through the Kerameikos, the district inhabited by potters and other artisans who regarded Prometheus and Hephaestus as patrons.

For compact space | compact 2-dimensional surfaces without boundary ( topology ) | boundary, if every loop can be continuously tightened to a point, then the surface is topologically Homeomorphism | homeomorphic to a 2-sphere ( usually just called a sphere ).

For instance, in the string " Texts for experts ", matches the " ex " in " experts " but not in " Texts " ( because the " ex " occurs inside a word and not immediately after a word boundary ).

For unknown reasons the treaty was not filed with the United Nations and nobody outside Iraq and Saudi Arabia was notified of the change or shown maps with details of the new boundary.

For a dawning sense of illumination occurs in consequence of two events which, as so often in Malraux, suddenly confront a character with the existential question of the nature and value of human life.

For it is clear that the total number of ordinary intersections of C and Af must be even ( otherwise, starting in the interior of C, Af could not finally return to the interior ), and the center of rotation at T is the argument of the function, not a value.

For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as

For this reason, orbitals with the same value of n are said to comprise a " shell ".

For the specific heats at least, the limiting value itself is definitely zero, as borne out by experiments to below 10 K. Even the less detailed Einstein model shows this curious drop in specific heats.

For instance, " LOW " and " LOSS " would be treated as the same variable, and attempting to assign a value to " LOSS " would overwrite any value assigned to " LOW.

For 160 years Wirt's account was taken at face value.

For given nonzero integers a and b there is a nonzero integer of minimal absolute value among all those of the form ax + by with x and y integers ; one can assume d > 0 by changing the signs of both s and t if necessary.

For instance during Operation Enduring Freedom the United States attacked targets of very low monetary value with cruise missiles, which led many to question the efficiency of the weapon.

For example, sewage sludge has a low but significant calorific value, and burns to give ash containing minerals useful in the clinker matrix.

For example, if the static compression ratio is 10: 1, and the dynamic compression ratio is 7. 5: 1, a useful value for cylinder pressure would be ( 7. 5 )^ 1. 3 × atmospheric pressure, or 13. 7 bar.

For example, Dalton assumed that water's formula was HO, giving the atomic weight of oxygen as eight times that of hydrogen, instead of the modern value of about 16.

; Time-variant: For An operational system, the stored data contains the current value.

For instance, there is no instruction to load an arbitrary “ immediate ” value into an accumulator ( although memory reference instructions do encode such a value to form an effective address ).

For example, Duncan Kennedy, in explicit reference to semiotics and deconstruction procedures, maintains that various legal doctrines are constructed around the binary pairs of opposed concepts, each of which with a claim upon intuitive and formal forms of reasoning that must be made explicit, not only in their meaning but also its relative value, and criticized.

For a decision which generates multiple cash flows in multiple time periods, all the cash flows must be discounted and then summed into a single net present value.

For a given quantity of a consumer good, the point on the demand curve indicates the value, or marginal utility, to consumers for that unit.

For example, for any given value of x it is true that

For a total eclipse, this value is always greater than or equal to one.

For instance the letter ⟨ e ⟩ in the word cottage indicates that the preceding ⟨ g ⟩ is pronounced, rather than the more common value of ⟨ g ⟩ in word-final position as the sound, such as in tag.

For example, the letter ⟨ i ⟩ in the word cinema has a sound-representing function ( representing the sound ) and a pronunciation-marking function ( marking the ⟨ c ⟩ as having the value opposed to the value ).