I know the word is very familiar - you, and even i, use it almost everyday in doing calculations ranging from simPle to comPlex ones. But it really confuses me.

When they say a quantity is ProPortional to another, what exactly do they mean? I'm asking because i've seen it Portray different meanings in different toPics.

For examPle, (1) they say the temPerature of any body is ProPortional to its average kinetic energy.
I think i can rightly deduce from that, that temPerature = average kinetic energy. Here, ProPortionality Portrays EQUALITY.

(2) i was reading triangles and their rules: they said some sides were ProPortional, i.e. a side of one triangle is in ProPortion with a side of the other triangle, but this didn't mean i could equate the two directly.

What does ProPortionality actually mean? Which word can i rePlace it with?



Cc. TeemPakguy, johnyjohn22, dejt4u, thankyoujesus, kamarnaut, other maths & science gurus.

Geofavor:
I know the word is very familiar - you, and even i, use it almost everyday in doing calculations ranging from simPle to comPlex ones. But it really confuses me.

When they say a quantity is ProPortional to another, what exactly do they mean? I'm asking because i've seen it Portray different meanings in different toPics.

For examPle, (1) they say the temPerature of any body is ProPortional to its average kinetic energy.
I think i can rightly deduce from that, that temPerature = average kinetic energy. Here, ProPortionality Portrays EQUALITY.

(2) i was reading triangles and their rules: they said some sides were ProPortional, i.e. a side of one triangle is in ProPortion with a side of the other triangle, but this didn't mean i could equate the two directly.

What does ProPortionality actually mean? Which word can i rePlace it with?



Cc. TeemPakguy, johnyjohn22, dejt4u, thankyoujesus, kamarnaut, other maths & science gurus.

Proportionality is used to show the relationship, connection and familiarity with variables, objects, things etc. Proportionality can be direct, indirect or inverse, joint and partial.

thankyouJesus:
Proportionality is used to show the relationship, connection and familiarity with variables, objects, things etc. Proportionality can br direct, indirect or inverse, joint or partial.

thanks. i know these ones. All these are covered under variations. But it's not in all cases that it is specified as either direct or inverse.

If i say something is proportional to something else, what does it mean?

Geofavor:
I know the word is very familiar - you, and even i, use it almost everyday in doing calculations ranging from simPle to comPlex ones. But it really confuses me.

When they say a quantity is ProPortional to another, what exactly do they mean? I'm asking because i've seen it Portray different meanings in different toPics.

For examPle, (1) they say the temPerature of any body is ProPortional to its average kinetic energy.
I think i can rightly deduce from that, that temPerature = average kinetic energy. Here, ProPortionality Portrays EQUALITY.

(2) i was reading triangles and their rules: they said some sides were ProPortional, i.e. a side of one triangle is in ProPortion with a side of the other triangle, but this didn't mean i could equate the two directly.

What does ProPortionality actually mean? Which word can i rePlace it with?



Cc. TeemPakguy, johnyjohn22, dejt4u, thankyoujesus, kamarnaut, other maths & science gurus.

When they say a quantity is ProPortional to another, what exactly do they mean? It means they are related under certain conditions.
I think i can rightly deduce from that, that temPerature = average kinetic energy. You left out the condition (proportionality constant), you are partially correct.
i was reading triangles and their rules: they said some sides were ProPortional, i.e. a side of one triangle is in ProPortion with a side of the other triangle, but this didn't mean i could equate the two directly. Taking right angle as a case study, the sides are in proportion to one another in 1:1:root2. Draw any right angle triangle of your choice, label the sides, find the last side, find their ratio.
In conclusion, proportion shows relationship. What about the Physics thread?

thankyouJesus:
When they say a quantity is ProPortional to another, what exactly do they mean?

---

It means they are related under certain conditions.

Can you pls explain it mathematically

I think i can rightly deduce from that, that temPerature = average kinetic energy.

---

You left out the condition (proportionality constant), you are partially correct.

does this mean that the constant, in this case, is unity?

i was reading triangles and their rules: they said some sides were ProPortional, i.e. a side of one triangle is in ProPortion with a side of another triangle, but this didn't mean i could equate the two directly.

---

Taking right angle as a case study, the sides are in proportion to one another in 1:1:root2. Draw any right angle triangle of your choice, label the sides, find the last side, find their ratio.
In conclusion, proportion shows relationship. What about the Physics thread?

pls take a look at the emboldened again

Geofavor:

Can you pls explain it mathematically


does this mean that the constant, in this case, is unity?


pls take a look at the emboldened again

Demand~Supply (price is the proportionality factor). Unity? Probably. For the triangle, yes, if and only if they are silmilar.

Okay, i am going to try and help you get the intuition behind proportionality.

proportionality means that there is a fixed rate of change between two objects. which is why in variation topics, they are always related by a constant. to show that, if one increases a a certain size, the second will equally increase a similar size.

You just said that Temperature = kinetic energy.
no it doesn't proportionality does not allow us to assume that something is equal to other. It is merely a tool for hypothesis. when you find a relationship between two objects, such that changing the amount of one will cause a similar, fixed change in the other. for instance, it is seen that when observing particle motion in a fluid,(Brownian motion) that the speed of the particles increased as the fluid was heated. hence temperature is related to kinetic energy since kinetic energy itself is related to the speed of masses. if the relationship is plotted on a line, a straight line results. so we can find that the slope is in fact, a constant. as in, dy/dx = some constant.

at this point, we can say, that temperature is indeed proportional to the other because a change of any size, in one, will lead to a similar change, in the other one.

sides of a triangle are proportional because if you increase one side, the others have to be increased as well for it to maintain the same shape.

thankyouJesus:
Demand~Supply (price is the proportionality factor). Unity? Probably. For the triangle, yes, if and only if they are silmilar.

alright, thanks so much. I'll create the physics thread as soon as i get better(i've been quite under the weather).

Teempakguy:
Okay, i am going to try and help you get the intuition behind proportionality.

proportionality means that there is a fixed rate of change between two objects. which is why in variation topics, they are always related by a constant. to show that, if one increases a a certain size, the second will equally increase a similar size.

You just said that Temperature = kinetic energy.
no it doesn't proportionality does not allow us to assume that something is equal to other. It is merely a tool for hypothesis. when you find a relationship between two objects, such that changing the amount of one will cause a similar, fixed change in the other. for instance, it is seen that when observing particle motion in a fluid,(Brownian motion) that the speed of the particles increased as the fluid was heated. hence temperature is related to kinetic energy since kinetic energy itself is related to the speed of masses. if the relationship is plotted on a line, a straight line results. so we can find that the slope is in fact, a constant. as in, dy/dx = some constant.

at this point, we can say, that temperature is indeed proportional to the other because a change of any size, in one, will lead to a similar change, in the other one.

sides of a triangle are proportional because if you increase one side, the others have to be increased as well for it to maintain the same shape.

you nailed it, mhen. Thanks!

Geofavor:

alright, thanks so much. I'll create the physics thread as soon as i get better(i've been quite under the weather).

so sorry, take care of yourself o