How To Use Equilateral In A Sentence

This is constructed by dividing a line into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment.

Figure 6 shows an equilateral triangle and a rhombus that circumscribe the same unit circle.

An equilateral triangle produces one of the observed cropcircle patterns; three isosceles triangles generate the other cropcircle geometries.

The faces of the polyhedron appear to consist of two equilateral triangles and six somewhat irregular pentagons.

Because the next most important angle to the right angle is the twothirds of a right angle; that is, the angle of an equilateral triangle.
The British and the Metric Systems

An equilateral triangle would be formed with its associated 60 degree angle.

The national flag consists of a square red field with a white equilateral cross at its center.

For example, we know that a circle is somehow more symmetrical than a equilateral triangle.

Euclid was able to draw an equilateral triangle, square, pentagon and hexagon, but recall that the heptagon (which has seven sides) and the nonagon (nine) eluded him.
HERE’S LOOKING AT EUCLID

The angles are equal, for ABC is equilateral.

Richardson, Taylor and Tomlinson are scattered, forming a sort of equilateral triangle.
Veterans Keep Jets Grounded

The form of that portion of the base of the bladder which is named "trigone vesical" constitutes an equilateral triangle, and may be described by two lines drawn from the vesical orifice to both openings of the ureters, and another line reaching transversely between the latter.
Surgical Anatomy

He also found another solution where the three bodies were at the vertices of an equilateral triangle.

In the first course, there was a shoulder of mutton cut into an equilateral triangle, a piece of beef into a rhomboides, and a pudding into a cycloid.
Gulliver's Travels into Several Remote Nations of the World

The real elements are two triangles, the rectangular isosceles which has but one form, and the most beautiful of the many forms of scalene, which is half of an equilateral triangle.
Timaeus

Ensure that the octagon is equilateral, meaning all sides on the ground have the same length.
5. Construction of ferrocement reservoirs

From the moment that grand trine appeared in the sky—an equilateral triangle like the great pyramids—it was our turn to clean house.
Surrender the Dark

Euclid was able to draw an equilateral triangle, square, pentagon and hexagon, but recall that the heptagon (which has seven sides) and the nonagon (nine) eluded him.
HERE’S LOOKING AT EUCLID

For instance, in the particular case of equilateral triangles it is true to say, not only that 'all equilateral triangles are equiangular,' but also that 'all equiangular triangles are equilateral.'
Deductive Logic

For example, is the attribute of being an equilateral triangle the same as the attribute of being an equiangular triangle?

construct an equilateral triangle

a tiny mining company working claims in the remote "equilateral" cluster of asteroids far out in Jupiter's orbit.
Gold in the Sky

Shell comparatively thin, and light and compressed valves; circular, sometimes oblique and equilateral; ribs twentyfour, marked on the outside with concentric squamose lines of growth, which are undulating, the last of which are strong; lower valve less convex than the upper.
Report of the NorthCarolina Geological Survey. Agriculture of the Eastern Counties: Together with Descriptions of the Fossils of the Marl Beds

Using these simple tools they could construct equilateral triangles and hexagons and they could bisect any angle.

How can anyone say that a scalene and an equilateral are really the same "kind"!
May 16th, 2009

The design radiates symmetrically from a central point and is constructed from a pattern of circles, equilateral triangles, squares, hexagons and/or sixpointed stars.

With the help of square, rhombus, rectangle, parallelogram, trapezium, equilateral, isosceles, diamond and kite shapes the direct and indirect approaches to teach the Pythagoras Theorem and other mathematical concepts is possible.

It happened that the Lancashire Queen, the shore at Turner's Shipyard, and the Solano Wharf were the corners of a big equilateral triangle.
THE SIEGE OF THE 'LANCASHIRE QUEEN'

The most interesting results show, with a very ingenious proof, that an equilateral triangle has a greater area than any isosceles or scalene triangle with the same perimeter.

Crosssections are in the shape of circles, ovals, squares, rectangles, equilateral triangles or regular polygons.

A regular octahedron has faces that are all equilateral triangles.

The hieroglyphical senary (the double equilateral triangle) is the symbol of Deity.
Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry

The design radiates symmetrically from a central point and is constructed from a pattern of circles, equilateral triangles, squares, hexagons and/or sixpointed stars.

Thus it is as true to say that 'All equiangular triangles are equilateral' as that 'All equilateral triangles are equiangular.'
Deductive Logic

As an equilateral triangle rolls over one catenary, it ends up bumping into the next catenary

Be there or be an equilateral tetragon with four eightpoint angles.
This is what Super Tuesday means, right?

Crosssections are in the shape of circles, ovals, squares, rectangles, equilateral triangles or regular polygons.

The design exclusively improves mechanical ways. Uses a suit of power source to drive two inequilateral arm's propulsions and successfully solves mutual interference.

For a given individual, the values of the three coefficients in the ancestry vector q are given by the distances to each of the three sides of the equilateral triangle.

The sides of this equilateral triangle will be five million kilometres long.

Obtained by the rotation of 60 ° of two equilateral triangles superimposed and spaced in height, the form appears simple but at the same time full of spatial complexity.
SwingUp by AquiliAlberg for Serralunga

Naturally, the axes form equilateral triangles  27 of them.

Pseudopecten dentatus, however, is prosocline, more equilateral and flaring, and lacks shagreen or nearshagreen microornament.

Bridge of the nose high and straight, from Biduan to Erjian and for the equilateral triangle.

The faces of the first three of these are composed of equilateral triangles, and each face is itself composed of six elemental (scalene) half equilateral rightangled triangles, whose sides are in a proportion of
Plato's Timaeus

Its outline roughly forms an equilateral triangle.

The cleaning layer has fully reticulated pores in a uniform network of substantially equilateral cells 34, such as tetrahedrons, truncated octahedrons and decahedrons.

The earliest symbols for the Trinity were abstract: the equilateral triangle, sometimes embellished with rays; an eye enclosed within a triangle, referring to the allseeing eye of God watching from the Trinity; the triangle enclosing a circle, suggesting the eternity of the Trinity; three interlocking circles to imply equality, unity, and eternity in the persons of the Trinity; or three equal intertwining arches, the triquetra, an early Christian emblem for the Trinity.
A Handbook of Symbols in Christian Art

An equilateral triangle of side length one is called a unit triangle.

But the image of the centroid of the equilateral triangle (which is, of course, the point of intersection of its medians) will be different, as indicated in Figure 6.

The simplest way to see why this assertion is true is to observe that any triangle in the plane can be mapped by an invertible affine transformation to an equilateral triangle.

For example, three Woolworths sites around Birmingham form an exact equilateral triangle (Wolverhampton, Lichfield and Birmingham stores) and if the base of the triangle is extended, it forms a 173.8 mile line linking the Conway and Luton stores.
Boing Boing

Any given triangle, either imagined or on paper, must either be acute, right, or obtuse, and either scalene, isosceles, or equilateral, and so any given triangle cannot represent all triangles.

Use your protractor to construct an equilateral triangle.

The theorem thus implies existence of the total of 18 equilateral triangles.

For example, a level 1 question asked why a certain figure was an equilateral triangle.

In 1772, J.L. Lagrange identified a periodic orbit in which three masses are at the corners of an equilateral triangle.

As long as the three triangles are equilateral, the ‘midpoint ‘triangle is also equilateral.’

A square is distinguished from other polygons by being foursided, equilateral, and equiangular.

One way to draw a Reuleaux triangle is to start with an equilateral triangle, which has three sides of equal length.

Thus all equilateral triangles are equiangular triangles; but in one case they are named from the equality of their angles, and in the other from the equality of their sides.
Logic Deductive and Inductive

Three  sided equilateral triangle that can be customized by dragging any selection handle.

The vibration exciter and geophone were placed near the burrow with burrow opening, exciter and geophone occupying the three corners of an equilateral triangle having sides one meter in length.

Figure 6 shows an equilateral triangle and a rhombus that circumscribe the same unit circle.

Its outline roughly forms an equilateral triangle.

Join five equilateral triangles together and you have the first part of an icosahedron C.
HERE’S LOOKING AT EUCLID

Yet being red should not be analysed into being coloured plus something else, in the way that being square can be analysed as being quadrilateral plus being equilateral and equiangular.

These five remarkable solids  tetrahedron, cube, octahedron, dodecahedron, icosahedron  have faces that are congruent equilateral polygons.

Judging the paintings, he said that straight lines, curves and equilateral triangles, involved in the drawing, could shape the children's handwriting.

From the moment that grand trine appeared in the sky—an equilateral triangle like the great pyramids—it was our turn to clean house.
Surrender the Dark

How can anyone say that a scalene and an equilateral are really the same "kind"!
May 16th, 2009

Its outline roughly forms an equilateral triangle.

The Von Koch snowflake is a fractal which is constructed from an equilateral triangle as follows.

Then divide it into three equal pieces, and replace the middle piece with the other two sides of the equilateral triangle that has this middle piece as its base.

For example, if all the equilateral triangles are all the equiangular, we know at once that all nonequilateral triangles are also nonequiangular.
Deductive Logic

equilateral triangles are triangles of equal edge lengths

This is constructed by dividing a line into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment.

If each edge has the same length and each face is an equilateral triangle, the result is a regular tetrahedron  one of the Platonic solids.

The materials of first experiment contain easily named shapes and the shapes not easy to name, with respectively fivepointed star shape, round, arrows, equilateral triangle, square.

For example, if you enter 1, 3, 6, 10, 15, the server will tell you that is sequence A000217, the triangular numbers (these are the number of objects that can form an equilateral triangle like the standard arrangement of bowling pins.)
An Important AT&T Legacy Finds a New Home « Steve Wildstrom on Tech

Although it is impossible to inscribe a regular pentagon in a square, an equilateral pentagon can be inscribed in two ways.

In the first course there was a shoulder of mutton, cut into an equilateral triangle, a piece of beef into a rhomboides, and a pudding into a cycloid.
Gulliver's Travels

Now, both the original Asymmetric Propeller and Napoleon's theorem start with three equilateral triangles and discover the fourth one by construction.

One way to draw this is to start with an equilateral triangle, which has three sides of equal length.

These five remarkable solids  tetrahedron, cube, octahedron, dodecahedron, icosahedron  have faces that are congruent equilateral polygons.

Each collects a cedar twig from the top of a tree, four equilateral triangular cuts are made with an archaic stone knife, and the twig is snapped off.
The Congress of Women: Held in the Woman's Building, World's Columbian Exposition, Chicago, U. S. A., 1893, With Portraits, Biographies and Addresses

A square is distinguished from other polygons by being foursided, equilateral, and equiangular.
Determinates vs. Determinables

Shell inequivalve and nearly inequilateral; free or adherent resting on one valve; beaks central, straight ligament internal; muscular impression single and behind the centre; hinge usually without teeth.
Report of the NorthCarolina Geological Survey. Agriculture of the Eastern Counties: Together with Descriptions of the Fossils of the Marl Beds

The third regular polygon is the equilateral triangle, and two of them joined make a diamond.

Using these simple tools they could construct equilateral triangles and hexagons and they could bisect any angle.

The Hindus I believe to have been the first who symbolised by an equilateral triangle their peculiar cult, the YoniLinga: in their temple architecture, it became either a conoid or a perfect pyramid.
Personal Narrative of a Pilgrimage to AlMadinah and Meccah

The most interesting results show, with a very ingenious proof, that an equilateral triangle has a greater area than any isosceles or scalene triangle with the same perimeter.

For example, it's possible to slice a square into four angular pieces that can be rearranged into an equilateral triangle.

The back of a second, kneeling Magus and of the seated Virgin supporting the Child form two sides of an equilateral triangle located plumb in the centre of the design.