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jbriggs444

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that

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S.G. Janssens

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He enjoys smooth structures.Why architect didn't told them to incline the roof at 30° or 60° etc and told them the length of roof

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jbriggs444

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Because the carpenter has a framing square, not a protractor.Why architect didn't told them to incline the roof at 30° or 60° etc and told them the length of roof

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youBecause the carpenter has a framing square, not a protractor.

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jbriggs444

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What is it that you are really trying to ask?Okk then you mean that they tell them the ratio of raise to far like 3:1 or 2:1 and they use this ratio to make the roof, but then 800cm/400cm and 40cm/20cm will also be 2:1, then how they will decide the lengths

Slope is what it is. Whether we choose to describe it as "rise over horizontal run", "rise over diagonal run", "angle from the horizontal", "angle from the vertical", "percent grade" does not change it. But at the end of the day we still want to come up with an agreement between the architect and the carpenter on how to describe it so that the carpenter builds what the architect intends.

None of which has much to do with the length of the rafters except that we may also need to come up with a way to communicate that. Cubits, rods, feet, inches, meters, centimers, ... And a way to estimate that (e.g. Pythagoras theorem).

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Mark44

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The Theorem of Pythagoras has been around for more than 2000 years. If the base and altitude of a right triangle are known, it's easy to compute the hypotenuse.Okk then you mean that they tell them the ratio of raise to far like 3:1 or 2:1 and they use this ratio to make the roof, but then 800cm/400cm and 40cm/20cm will also be 2:1, then how they will decide the lengths

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The Theorem of Pythagoras has been around for more than 2000 years. If the base and altitude of a right triangle are known, it's easy to compute the hypotenuse.

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jbriggs444

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So tell us. How inclined must it be?"To make the roof" means how inclined it must be

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member 587159

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You said that slope is used to tell how steeper is line or roof , you said that carpenter were not having protractor so that they can inclined them just by saying the angle , therefore architects defined slope to get the [approximate] idea of steepness. So I think that they tell them the rise and far ratio by telling them lengths of rise and far(as per the tan of the angle calculated by them) . With your opinion I think that architect may knew trigonometry at that time. so basically I think that they have introduced slope more importantly to display the rate of change graphically and mathematically. And steepness of roof or road may be its 2nd application, I dont have any evidance to prove it but I think introducing slope for rate of change is more appropriate, what's your opinionSo tell us. How inclined must it be?

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I just want to know that how founder of slope must have introduced this concept.You said that slope is used to tell how steeper is line or roof , you said that carpenter were not having protractor so that they can inclined them just by saying the angle , therefore architects defined slope to get the [approximate] idea of steepness. So I think that they tell them the rise and far ratio by telling them lengths of rise and far(as per the tan of the angle calculated by them) . With your opinion I think that architect may knew trigonometry at that time. so basically I think that they have introduced slope more importantly to display the rate of change graphically and mathematically. And steepness of roof or road may be its 2nd application, I dont have any evidance to prove it but I think introducing slope for rate of change is more appropriate, what's your opinion

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jbriggs444

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What is the motivation for the question? Why does it matter?

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Yes I got it but can you give me the example for the architect and the carpenter . How architect told carpenter to make the roof steeper by telling him the slope. I totally agree with your answer but an example can make it more clearer. I read on wikipedia that slope is applied to the road by telling the % , 100% means 45° Inclined. I think similarly architects may have used some way to define steepness to the carpenter

What is the motivation for the question? Why does it matter?

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FactChecker

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yes , therefore I think that slope may be introduced to show rate of change mathematically and geometrically.

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I believe slope was first formalized by Newton to solve mechanics problems.

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Mee too, rate of change

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chiro

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It's just a mathematical definition looking at a rate of change.

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In electronics, very often we have to work with

In most applications, we select a certain "operational point" on this non-linear characteristic using DC quantities (voltages and/or currents).

Then, it is very important to know the SLOPE of the characteristic in this particular operational point (bias point).

Fore example, for bipolar transistor amplifiers the slope of the voltage-in and current-out characteristic is the so-called "transconductance" - a key parameter for gain calculations.

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