# hypotenuse

## Definitions

• WordNet 3.6
• n hypotenuse the side of a right triangle opposite the right angle
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Webster's Revised Unabridged Dictionary
• n Hypotenuse (Geom) The side of a right-angled triangle that is opposite to the right angle.
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Century Dictionary and Cyclopedia
• n hypotenuse In geometry, the side of a right-angled triangle opposite the right angle.
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Chambers's Twentieth Century Dictionary
• n Hypotenuse hī-pot′en-ūs or hip- the side of a right-angled triangle opposite to the right angle.
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## Etymology

Webster's Revised Unabridged Dictionary
L. hypotenusa, Gr. , prob., subtending (sc. ), fr. to stretch under, subtend; under + to stretch. See Subtend
Chambers's Twentieth Century Dictionary
Fr.,—Gr. hypoteinousa (grammē), lit. (a line) 'which stretches under'—hypo, under, teinein, to stretch.

## Usage

### In literature:

It usually takes a hypotenuse a long time to discover that it is the longest side of a triangle.
"Options" by O. Henry
A, walking from corner to corner, may be said to diangulate the hypotenuse of the meadow.
"My Discovery of England" by Stephen Leacock
You would not write your name in pencil across the hypotenuse of a right-angled triangle.
"A Portrait of the Artist as a Young Man" by James Joyce
Large spaced drops plumbed a gleaming hypotenuse between the rooftops and the streets.
"Erik Dorn" by Ben Hecht
Hypotenuses: in Odonata; the simple or broken cross-vein between media 4, and cubitus 1, forming outer boundary of triangle.
"Explanation of Terms Used in Entomology" by John. B. Smith
Therefore the hypotenuse is 43 ft. 4 in.
"The Canterbury Puzzles" by Henry Ernest Dudeney
Ask me about the square on the hypotenuse of a right-angled triangle.
"The Boy Grew Older" by Heywood Broun
Is a triangular shaped town, the hypotenuse being formed by the Mississippi river.
"Fifty Years In The Northwest" by William Henry Carman Folsom
But QP is the hypotenuse of a triangle PP1Q with a right angle P1.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
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### In news:

Square of the Hypotenuse .
Vertical Installation - 6" Wide Channel Triangular back to shaft (42"+/-) Hypotenuse - 76" Tip to Tip.
Somebody has to be the hypotenuse, loving the wrong person, giving too much or too little.
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### In science:

Let we have two functions f and f ′ on two copies of the grid ∆n such that λ, the tuple of increments of f along the hypotenuse, is also the tuple of increments of f ′ along the base of the triangle.
A simple proof of associativity and commutativity of LR-coefficients (or the hive ring)
Similarly, the triangle containing an exterior edge of G is endowed with the metric of half a unit square (split on its diagonal, with the exterior edge as the hypotenuse).
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
This produces the approximate value 590 for the hypotenuse immediately, after which a few calculations yield 591 < γ < 592.
Archimedes' calculations of square roots
For example, it is easy to see that it contains an isosceles right triangle (dented along the hypotenuse).
The DNA Inequality in Non-Convex Regions
But then C must exit K ′ from the hypotenuse.
The Octagonal PET II: The Topology of the Limit Sets
KL → p0n ¯n, which determines the height of the triangle is theoretically the cleanest, but experiment is many orders of magnitude short of the SMpredicted level. K+ → p+n ¯n, which determines the hypotenuse, is nearly as clean as KL → p0n ¯n and has been observed.
Rare K decay: results and prospects
In that case, since β is orthogonal to α0 it is a right triangle with hypotenuse α.
The geometry at infinity of a hyperbolic Riemann surface of infinite type
It follows that, by moving a small distance from Q = σc (0) along δ to a point B , there is a point E on α0 so that arcs QB , BE , and EQ form a right triangle, with right angle at E , and hypotenuse QB .
The geometry at infinity of a hyperbolic Riemann surface of infinite type
Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality.
Pythagorean Triples and a New Pythagorean Theorem
When a right triangle with legs a, b and hypotenuse c is given, there are just two squares (Figures 3a, 3b), the “harmonic” square of side h, and the “symphonic” square of side s.
Pythagorean Triples and a New Pythagorean Theorem
PPT in which the hypotenuse and the sum of the legs are both squares.
Pythagorean Triples and a New Pythagorean Theorem
The inhomogeneous estimates can be put into three groups in rising order of diﬃculty: the inner part of ∆OAB , the two catheti OA and OB , and the hypotenuse AB .
Strichartz estimates for the kinetic transport equation
We suppose now that P lies on the hypotenuse of ∆OAB in Figure 1 and that it also belongs to E0 .
Strichartz estimates for the kinetic transport equation
Points are marked according to whether the hypotenuse is prime ( ) or composite ( ).
From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits
Elementary considerations then force the hypotenuse z to be odd, and x and y to be of opposite parity; we assume henceforth that x is odd and y is even.
From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits
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