The hypotenuse is the side of the triangle which is the longest...e.g. think of a right angled triangle...the two lines which are at right angles to one another, are the adjacent and opposite lines. The line running between to two ends of those lines is the hypotenuse.
The hypotenuse is the side of the triangle which is the longest...e.g. think of a right angled triangle...the two lines which are at right angles to one another, are the adjacent and opposite lines. The line running between to two ends of those lines is the hypotenuse.
"Once upon a time in an Indian village, there lived three squaws. Two squaws had young sons who were very overweight. The first squaw, whose son weighed 150 pounds, always placed her son on a bear hide near a pine grove; the second squaw, whose son also weighed 150 pounds, put her son on a moose hide in the shade of a large oak tree; but the third squaw, who was expecting the birth of her first son, always rested on a hippopotamus hide beside a bubbling brook. Her weight? 300 pounds! To this day, mathematicians give credit to these women and their children for proving the Pythagorean Theorem, because you see: The squaw of the hippopotamus is equal to the sons of the squaws of the other two hides."
"Once upon a time in an Indian village, there lived three squaws. Two squaws had young sons who were very overweight. The first squaw, whose son weighed 150 pounds, always placed her son on a bear hide near a pine grove; the second squaw, whose son also weighed 150 pounds, put her son on a moose hide in the shade of a large oak tree; but the third squaw, who was expecting the birth of her first son, always rested on a hippopotamus hide beside a bubbling brook. Her weight? 300 pounds! To this day, mathematicians give credit to these women and their children for proving the Pythagorean Theorem, because you see: The squaw of the hippopotamus is equal to the sons of the squaws of the other two hides."
Thank goodness Pythagorus isn't alive to see this sacrilege.
The hypotenuse is the side of the triangle which is the longest...e.g. think of a right angled triangle...the two lines which are at right angles to one another, are the adjacent and opposite lines. The line running between to two ends of those lines is the hypotenuse.
...
The squaw of the hippopotamus is equal to the sons of the squaws of the other two hides."
Nice rendition of the tale.
Excuse the digression but it reminds me of another story ...
Preliminary-
Pythagoras' theorem states that for a right triangle with sides a, b, c (the hypotenuse), then a^2+b^2=c^2. A Pythagorean triad is a set of 3 sides for a right triangle e.g. 3,4,5 where 3^2+4^2=5^2 or 9+16=25.
In those days, Liethagoras, who was jealous of Pythagoras' fame, noticed an interesting connection between Pythagorean triads and proposed a much simpler theorem for right-angled triangles: a^2=b+c.
3,4,5 ---> 3^2=4+5
5,12,13 ---> 5^2=12+13
7,24,25 ---> 7^2=24+25
However, his fame was short-lived when it was brought to Pythagoras' attention and he laughed off the proposition.
For anyone interested, under what condition is Liethagoras correct?
Digital calculators were accounted for by five on each hand and only a small fraction of the class could use these accurately in any case but we at least had trig and log tables.
Barry
Hi,
Aha yes, now did anyone use Chamber's 7 figure log tables? I still have a copy somewhere, with my Sun Hemmi slide rule.
The first calculator I ever had was a Texas Instruments SR-50 bought off a bloke who came around to my workplace (Email at Rosebery) in about 1975. He was flogging that one and a Hewlett Packard which had Reverse Polish Notation. I didn't know any forward Polish, much less RPN, so I bought the TI. I remember it cost about $350, which was an enormous amount in those days, but I claimed it on tax. I was hooked. I used to take it to meetings and calculate away, giving everyone else the pip.
Excuse the digression but it reminds me of another story ...
Preliminary-
Pythagoras' theorem states that for a right triangle with sides a, b, c (the hypotenuse), then a^2+b^2=c^2. A Pythagorean triad is a set of 3 sides for a right triangle e.g. 3,4,5 where 3^2+4^2=5^2 or 9+16=25.
In those days, Liethagoras, who was jealous of Pythagoras' fame, noticed an interesting connection between Pythagorean triads and proposed a much simpler theorem for right-angled triangles: a^2=b+c.
3,4,5 ---> 3^2=4+5
5,12,13 ---> 5^2=12+13
7,24,25 ---> 7^2=24+25
However, his fame was short-lived when it was brought to Pythagoras' attention and he laughed off the proposition.
For anyone interested, under what condition is Liethagoras correct?
Therefore can select
b = 2n^2+2n = n((2n+1)+1) = n(a+1)
c = 2n^2+2n+1 = b+1
However, the end result still works out the same.
For any odd integer a, you can always find two consecutive integers b,c to complete the triad.
e.g. a = 9
a = 2n+1 = 9 ---> n = 4
b = n(a+1) = 4(9+1) = 40
c = 40+1 = 41
Triad 9,40,41.
The first calculator I ever had was a Texas Instruments SR-50 bought off a bloke who came around to my workplace (Email at Rosebery) in about 1975. He was flogging that one and a Hewlett Packard which had Reverse Polish Notation. I didn't know any forward Polish, much less RPN, so I bought the TI. I remember it cost about $350, which was an enormous amount in those days, but I claimed it on tax. I was hooked. I used to take it to meetings and calculate away, giving everyone else the pip.
Cheers
My first calculator was bought for 29 pounds in 1963 when I was earning 21 pounds a week (for those who understand not LSD, $58 and $42 respectively). It did square roots with a key press. Its greatest problem was it ran from a peculiar battery that I could never find a replacement for so I could eventually only use it from a PS that I built.
My next calculator was a HP45? bought under student discount for about $250, I think, in 1970. It was great. I loved the RPN and even more the direct polar/cartesian conversion. This was handy as I was doing a measurement on a 36' whip aerial with an RF bridge and a B40 receiver and doing dozens of calcs by hand to plot a Smith Chart. Saved me about a week. I loaned the calculator to my son in 1978 and have not seen it since.
For those who never used RPN it was like entering the steps of a calculation in the reverse order then pressing the "Go" button to get an answer. way to Go!
sin is the standard abbreviation for sine which is the ratio of the opposite side of a right triangle divided by the hypotenuse.
Actually it's much simpler than that. Sine used to be the name of this greek guy who liked his vino too much and used to walk around in the weirdest of patterns. The name stuck and the rest is history. ... so says his mate "co".
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