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1
Mathematics and Its History
The area of a right-angled triangle the sides of which are rational numbers
cannot be a square number. This proposition, which is my own discovery, I have
at length succeeded in proving, though not without much labour and hard
thinking.
2
Diophantus of Alexandria: A Study in the History of Greek ...
THEOREMS AND PROBLEMS ON RATIONAL RIGHT-ANGLED TRIANGLES. i.
On No. 20 of the problems about right-angled triangles added by Bachet to Book
vi. ("To find a right-angled triangle such that its area is equal to a given number")
...
Sir Thomas Little Heath, 2012
3
More about Functions and Differentiation: Unit 6: ...
You may already be familiar with definitions of sine and cosine as ratios of sides
in a right-angled triangle. If you are, you must be wondering what connection
these have with the "unit circle" definitions just given. Here's a reminder of the ...
4
Year 10 Advanced Mathematics: Stage 5.3
In a right-angled triangle, the hypotenuse is the longest side (the side opposite
the right-angle). The opposite and adjacent sides depend on which angle we are
considering. The opposite side is opposite the angle and the adjacent side is
next ...
UNIT 1: Review of right angled triangle trigonometry EXCEL YEARS 9 & 1 0
ADVANCED MATHS Ch. 10, 10.1, p. 143 QUESTION 1 Evaluate correct to three
decimal places. a sin 75° = b tan34° = d tan65°07 = e cos105°36' = QUESTION 2
IfO° ...
6
A course of mathematics
If in a right-angled triangle, a perpendicular be drawn from the right angle to the
hypothenuse, and circles inscribed within the triangles on each side of it ; their
diameters will be to each other as the subtending sides of the right- angled
triangle.
Charles Hutton, Olinthus Gilbert Gregory, 1836
Hence for a right-angled triangle, G is j of the way from the right-angle along each
of the perpendicular sides, e.g. If the lamina is not uniform its centre of mass is
unlikely to be at the centroid. In other words, the centroid of a triangle is always ...
Linda Bostock, Suzanne Chandler, 1996
8
God Created the Integers: The Mathematical Breakthroughs ...
In future I shall say “right-angled triangle” simply, for brevity. 6 Diophantus here
tacitly assumes that, if and right-angled triangles be formed from (c, a), (c, b) and (
c, ) respectively, their areas are equal. The areas are of course and and it is easy
...
9
Intermediate Geometry: Experimental, Theoretical, Practical
A Right-angled Triangle is a triangle which has one of its angles a right angle,
e.g. ABC is a right-angled triangle, because L B = 1 rt. L . Ex. 1. — Draw a right-
angled triangle freehand. Ex. 2. — Construct a right-angled triangle. Constr. :
Draw a ...
These are called an acute-angled triangle, an obtuse-angled triangle and a right-
angled triangle. Acute-angled triangle: A triangle is said to be an acute-angled
triangle when each angles is acute, Le. less than 90°. In Figure 14.34, AABC is
an ...
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «RIGHT-ANGLED TRIANGLE»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
right-angled triangle w wiadomościach.
Explained: Hero of 'greatest battle ever fought on a river'
In his five-volume Comprehensive History of Assam, H K Barpujari described the final moments of Saraighat: “The right-angled triangle of the Brahmaputra ... «The Indian Express, Maj 15»
Ruby Tandoh's recipes for handmade, handheld pasties and pies
You're going to be folding one corner of the pastry diagonally across the filling to form a right-angled triangle, so try to add the cheesecake mixture with that in ... «The Guardian, Maj 15»
Getting the mathematics right on world peace
Pythagoras expressed it best when he said a2+b2=c2 for a right-angled triangle. Let the world be a and peace be b. Then world peace would be the square of ... «Hindustan Times, Kwi 15»
Spring Skywatching: Constellation Leo Comes in Like a Lion
As seen from the Northern Hemisphere, Leo consists of a sickle or reversed question mark on the right and a right-angled triangle on the left. The "period" at the ... «Yahoo News, Kwi 15»
The story of shunya
In 6th century BC, a mathematician named Pythagoras proved that the square of the hypotenuse of any right-angled triangle is the sum of the squares of its two ... «The Indian Express, Mar 15»
Putting two and two together
While we're mentioning the hypotenuse, you may well recall that it is 'the longest side of a right-angled triangle, opposite the right angle', but may not know the ... «OUPblog, Mar 15»
2500-year-old Pythagoras theorem helps to show when a patient …
Pythagoras theorem states that in a right-angled triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse (i.e the ... «Medical Xpress, Gru 14»
How triangles revolutionized mapmaking
In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Many triangles in real ... «The Week Magazine, Kwi 14»
Beautiful Geometry, by Eli Maor and Eugen Jost
There is wit, as in “25 + 25 = 49”, which displays a right-angled triangle with sides 7, 7 and 10; this may not work mathematically, but the artist quotes the painter ... «Times Higher Education, Mar 14»
Robert Emms interview: My bromance with Mark Addy and Jack …
In a right-angled triangle, a2 + b2 = c2 – the side opposite the right angle is the hypotenuse and that's equal to the squares of the other two sides of the triangle. «Big Issue, Lut 14»
