Posts by Hannibal lecter

Hannibal lecter · Help Me !

oh thanks for that golden information now I can use the protractor professional

but why when trying to extend them in my draw sheet they meet from up side?
they shouldn't meet right
I always draw the same lines angles and they meet!
is that because the direction of the second line maybe it called negative? or it's from another plane or what I know the parallel lines won't meet in the two directions

Hannibal lecter · Help Me !

Bob wrote:

In your diagram the line made by 100 degrees should slope away from the other line as 100 is obtuse. These lines are parallel.
Bob

But if O extend them from the top won't they meet?

Hannibal lecter · Help Me !

hi,
in this link :

https://mathcs.clarku.edu/%7Edjoyce/java/elements/bookVI/propVI4.html

I Quote from : Now, since the angle DCE equals the angle ABC, DC is parallel to FB. Again, since the angle ACB equals the angle DEC, AC is parallel to FE.
depending on the right link : (I.28) as you can see on the page in the right that blue link
that leads to proposition 28 book I (https://mathcs.clarku.edu/%7Edjoyce/java/elements/bookI/propI28.html)

the problem he is saying DCE equals the angle ABC but it's not like proposition 28 said
because DCE and ABC is corresponding angels which the proposition 28 didn't mention anything about it just talk about alternate angels,
so how cold they depend on something that in its turn didn't mention them or talk about!!!
please explain it's very necessary to me

Hannibal lecter · Help Me !

What is wrong in proposition 28 Book 1 of Euclid elements the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another
I can draw easily with handwrite on a papers two lines adds up two right angels but they are not parallel? So what's wrong?

and I draw an example in the following photo and here is the link and Quote of the proposition 28

proposition 28 book 1
If a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle on the same side, or the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another

the photo I draw and tried as u will see the straight line fall on the two lines and and draw the first left angel 100 degree and the other 80 so they add up to 180 but not parallel! the proposition consist of two sections the first section is clear and I understand it but after "or the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another.... is not clear"

Hannibal lecter · Help Me !

on MIF https://www.mathsisfun.com/geometry/triangles-similar-finding.html

in the SAS example "side, angle, side"
there is two triangles, he found that these two is similar
because thier ratios are equal
21 : 14 which is 3/2
and
15 : 10 which is 3/2

my problem is he divide Traingle1 Side over Traingle two Side
and divide the second side which is 15 of traingle 1 when the second side of the traingle two which is 10

but in Similar Topic on MIF https://www.mathsisfun.com/geometry/similar.html

in the Example named " Example: What is the missing length here?"
he divided the blue triangles with its sides themselves : 130/127 which is blue traingle side over blue traingle second side
and equal to ?/80 which is red side over red side

now how to check the similarity exactly by dividing one side of a traingle with the other traingle side? or using the same side of the traingle
for example traingle with side x1 and x2 and another traingle with side y1 and y2
the similarity check is using : x1 over y1 equal to x2 over y2
or : x1 over x2 equal to y1 over y2?

Hannibal lecter · Help Me !

Bob wrote:

Abot half way he gets to the formula
Then he takes the right angled triangle with shorter sides r and x, and enlarges it by a scale factor of yz so it becomes rxz by by xyz. He adds on other enlarged triangles.
Bob

why he enlarged the r and x by yz
What for?
And next step he enlarge the sides r and y by
z.(x^2+r^2)^1/2 Why exactly this equation?

Hannibal lecter · Help Me !

Bob wrote:

Try:
https://jscholarship.library.jhu.edu/bi … 623049.pdf
Bob

Mr Bob it's a useful book thank you so much

Hannibal lecter · Help Me !

In this YouTube link

https://youtu.be/6KPSmajeseI

He is talking about heron's proof
He is talking about scaling a traingle
Starting in minute 1:01

What is a traingle scaling and is there on MiF

Hannibal lecter · Help Me !

Bob wrote:

Napier is credited with the invention of logarithms. He wrote that book in Latin and Macdonald translated it into English. But the style and language is Napier's.
The table is a list of logarithmic values. Before the invention of computers and calculators, logarithms were used to enable calculations without the need for long multiplication and division. When I was at school we were given such a table and taught how to use them.
There's a page about him in Wiki: https://en.wikipedia.org/wiki/John_Napier
If you want to learn about logs then I recommend the MIF page:
https://www.mathsisfun.com/algebra/logarithms.html
Hope that helps,
Bob

Mr bob where can I found that table it's not there in MIF and tutorial for how to use it

Hannibal lecter · Help Me !

Jai Ganesh wrote:

Here's the link.

yes but there is a table where is that table the book is talking about table of logarithm

Hannibal lecter · Help Me !

Bob wrote:

Napier is credited with the invention of logarithms. He wrote that book in Latin and Macdonald translated it into English. But the style and language is Napier's.
The table is a list of logarithmic values. Before the invention of computers and calculators, logarithms were used to enable calculations without the need for long multiplication and division. When I was at school we were given such a table and taught how to use them.
There's a page about him in Wiki: https://en.wikipedia.org/wiki/John_Napier
If you want to learn about logs then I recommend the MIF page:
https://www.mathsisfun.com/algebra/logarithms.html
Hope that helps,
Bob

I didn't found the table in MIF can you send it to me here please

Hannibal lecter · Help Me !

Bob wrote:

Ok found it. Napier's language is not modern so it's tricky to follow what he is talking about. He seems to be talking in general terms about how accurately you might want to calculate something. So he uses examples where he leaves off the least significant digits without seriously affecting the quality of the result. In the Archimedes example he has a diameter divided into 497 parts ( =N say) so he reasons that the circumference should be divided into pi times N parts. If you take pi as 3.141 you get an answer that lies between 1562 and 1561.
Bob
ps. If you want to learn about logarithms (maybe after sines!) then look at MIF to get more up to date language.

when I do pi * 497 I find it's equal to 1561.37154883 to 1562
also in the book he is talking about a table which is that table? where can I find it

mr bob this book translation by WILLIAM RAE MACDONALD,
is there another better translation that understandable by students give me any another translation please

Hannibal lecter · Help Me !

Bob wrote:

Here's a way to find the centre by construction. You'll need a sharp pencil, a ruler and a compass (for drawing circles).
https://i.imgur.com/ve024Du.gif
In this diagram the starting point is the large green circle.
Draw any line that cuts the circle in two places, A and B. Extend the line at the B end.
With B as centre draw a smaller circle that cuts AB at C and D.
Set the compass to a larger radius; then with C as centre draw two arcs judging by eye where to make them**. Repeat from D so that these second arcs cut the first. Where these arcs cross gives the points E and F. ** So that the second arcs cross at E and F.
Join E to F and extend this line to cross the original circle at G.
Line EFG is perpendicular to AB. (You can easily prove this by considering the quadrilateral CFDE and showing it is a rhombus.)
So ABG is 90 and so AG is a diameter.
Repeat this process with a new line A'B' and construct a new diameter A'G'.
Where the two diameters intersect is the centre.
Bob

Mr Bob I want to find the center according to MIF using thales theorm only

Hannibal lecter · Help Me !

How yo 0lace Pi or any irrational numbers on a graph

Hannibal lecter · Help Me !

from this : https://www.mathsisfun.com/geometry/circle-theorems.html

my problem is when I draw a circle on a paper using circle template tool and trying to do these steps on MIF :

Finding a Circle's Center
finding as circles center
We can use this idea to find a circle's center:

draw a right angle from anywhere on the circle's circumference, then draw the diameter where the two legs hit the circle
do that again but for a different diameter
Where the diameters cross is the center!

I don't know how to draw a right angel from a circle circumference
how to know this angel would be 90 degree
is there any video illustrate these steps

Hannibal lecter · Help Me !

Example: Compare a square to a circle of width 3 m
Square's Area = w^2 = 3^2 = 9 m^2

Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = 7.2 m2

Circle's True Area = (Pi/4) × D2 = (Pi/4) × 32 = 7.07 m^22 (to 2 decimals)

The estimate of 7.2 m2 is not far off 7.07 m2

I found this in MIF link : https://www.mathsisfun.com/geometry/circle-area.html

it says area of a circle is = Pi/4 * r^2

but I used to use the formula only Pi * r^2
why the website multiply it by 1/4

I even didn't understand the headline : Comparing a Circle to a Square!!!
it said : A circle has about 80% of the area of a similar-width square.
how did he find that? maybe the circle is 70% of 50%
and how did he say : similar-width! it's first time I read about that term width of a circle

Hannibal lecter · Help Me !

Bob wrote:

I'm confused about what you want me to show. Are you able to give the complete reference for where you found this?
Bob

Mr bob I want an example to calculate a degree of an triangle with only using basic geometry and trigonometry without using moderns ways like we living in 600BC history, by steps and graphs diagrams please any triangle even with sides length 1

Hannibal lecter · Help Me !

Bob wrote:

hi HL,
I think the ancient Babylonians invented the angle measure of one degree so that a complete rotation is 360 degrees. I've not read a definite reason for this but there are two possible explanations: (1) The night sky advances by roughly one degree per night. This is because of the number of days in a year. I can explain this more precisely but there's no need to get sidetracked at the moment. (2) 360 has lots of factors, so is a 'nice' number with which to work.
Euclid's book (The Elements) shows, early on, how to show that the angle sum of a triangle is 180 degrees. If the triangle is equilateral then it has (by definition) rotational symmetry order 3, so each of the three angles must be 360/3 = 60.
There's something funny about your steps for making a diagram.
3. Extend the line segment BC to intersect the circle at a point D.
But with centre A and AB = AC the line BC 'crosses' the circle at two points, B and C ; so where is D? From then on I couldn't make any progress with the diagram.
There's a free download of a geometry program called Geogebra. This will enable you to create your own diagrams.
Bob

it's a robot answer I don't think it's accurate but it would be useful if it make that examples using graphs and drawing
can you make a diagram and images using any examples and any lengths of triangle just want to understand how they measure a degree using basic geometry and Pythagoras without using sine and cosine only ratios of side without calling them sine
like Thales and Archimedes did

Hannibal lecter · Help Me !

I was study that the some of angels of a triangle contain 180 degree
my problem is with the proof

please see this photo I marked up the angle by sky blue color it's 125 degree

now this is another photo figure about the triangle

now how could that angel which is 125 degree equal angel F?

by just looking it, it's look like B+C which is 125 degree
so F can't be 125 degree

I combined the two figures into one using pen and paper and see the photo :-

Hannibal lecter · Help Me !

The following is and example but it's without graphs
And figure or draws So I can't see :
Please Mr bob draw for me the steps I want see and imagine
If we are limited to the knowledge and techniques of geometry used in 600 BC, we can still use basic geometric constructions to find the angles of an equilateral triangle with side length 1.

Here's one possible method:

1. Draw an equilateral triangle ABC with side length 1.
2. Draw the circle centered at A with radius AB = AC = 1.
3. Extend the line segment BC to intersect the circle at a point D.
4. Draw the line segment AD, and label the point of intersection with BC as E.
5. Draw the line segment BE.
6. Draw the perpendicular bisector of line segment AB, and label the point of intersection with line segment BE as F.
7. Draw the line segment AF.
8. Draw the perpendicular bisector of line segment DE, and label the point of intersection with line segment AF as G.
9. Draw the line segment BG.
10. Label the point of intersection of line segments AF and BG as H.

Now, we can use the fact that triangle ABC is equilateral to show that angles AHB and AFB are both equal to 120 degrees. This is because triangle ABH is congruent to triangle ABF (by side-side-side), so angle AHB must be congruent to angle AFB.

Next, we can use the fact that line segment AH is the angle bisector of angle BAC to show that angle HAB is equal to angle HAC. This is a property of angle bisectors in triangles.

Finally, we can use the fact that angle HAB and angle HAC are complementary angles to show that each angle is 30 degrees. This is because angle HAB + angle HAC = angle BAC = 60 degrees (since triangle ABC is equilateral), so each angle must be 30 degrees.

Therefore, all three angles of the equilateral triangle with side length 1 are 30 degrees.

Hannibal lecter · Help Me !

Bob wrote:

is the 1 : 500,000 a scale? or a ratio?

Bob
ps. How are you getting on with trigonometry?

I am continuing then I'll study logarithmic finally

Hannibal lecter · Help Me !

How to calculate a degree of traingle
Sides is 1 length using basic geometry only and Pythagorean theorem without using sine and cosine like we are in 300 BC or 600 BC
I want any simple example
To understand how they were calculate degree in old times
Please this will help me a lot and a lot

Hannibal lecter · Help Me !

1/7 is interesting. When you divide by 7, if it doesn't divide exactly then there are 6 possible remainders. As you carry out the division, all 6 remainders occur. After that there can only be a repeated remainder so the division recurs with a cycle of 6 digits.
1/7 = 0.142857142857142857........

From this idea you can move on to realise that every fraction conversion to decimal must either terminate or recur.

How to find 0.142857 using pen and papers
I keep subtracting 1−0.7−0.07−0.07−0.07−0.07−0.007−0.007−0.0007−0.007−0.0007−0.00007−0.0007−0.0007−0.00007−0.0007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007−0.00007

Until the calculator exceed the maximum number
And I didn't get any of these values 0.142857

I know it's non terminated decimal but I can't even get the first numbers while doing reapeted subtracting as you tought me

Also when I do 1/4 I get 1−0.4−0.4−0.04−0.04
−0.04−0.04−0.04=0
But I don't get the results which is 0.25

Also with 3/4=0.75
Is 3−0.4−0.4−0.4−0.4−0.4
−0.4−0.4−0.04−0.04−0.04
−0.04−0.04=0
But I didn't get the value 0.75

Hannibal lecter · Help Me !

The distance between two towns on a map is 5 cm. If the real distance between the two towns is 25 km, what is the scale of the map?

it's in Question5 of this page :

https://www.mathopolis.com/questions/q.html?id=1710&t=mif&qs=1709_1710_1711_1712_1713_1714_1715_1716_3603_3604&site=1&ref=2f6e756d626572732f726174696f2e68746d6c&title=526174696f73#

on MIF

the question is talking about the distance between two city, the answer is B)

the scale of the map is 5 cm : 2,500,000 cm
Which is 1 : 500,000

is the 1 : 500,000 a scale? or a ratio?

at only this question I confused where is the ratio there

it's a scale as in Horse Example :- https://www.mathsisfun.com/numbers/ratio.html

this horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000

What is that ratio when we draw it at 1/10th normal size?

1500 : 2000 = 1500×1/10 : 2000×1/10
= 150 : 200

so it's a scale, it's the only question that I confused where is the ratio there is a two city on paper they are far 5 cm in real 25 km
where is the the ration there

Hannibal lecter · Help Me !

it's page 9 he is talking about 1562 and 1561

Math Is Fun Forum

#1 Re: Help Me ! » Euclid book 1 of elements proposition 28 » 2024-02-07 01:59:31

#2 Re: Help Me ! » Euclid book 1 of elements proposition 28 » 2024-01-26 16:42:02

#3 Help Me ! » conflict in some Euclid of elements book » 2024-01-25 09:57:37

#4 Help Me ! » Euclid book 1 of elements proposition 28 » 2024-01-25 08:59:12

#5 Help Me ! » How to Find if Triangles are Similar » 2023-08-31 22:22:43

#6 Re: Help Me ! » Visual heron's formula » 2023-08-10 22:06:40

#7 Re: Help Me ! » from napier book » 2023-08-09 22:05:24

#8 Help Me ! » Visual heron's formula » 2023-08-08 09:12:03

#9 Re: Help Me ! » from napier book » 2023-08-08 05:58:14

#10 Re: Help Me ! » from napier book » 2023-08-04 04:33:35

#11 Re: Help Me ! » from napier book » 2023-08-03 04:27:03

#12 Re: Help Me ! » from napier book » 2023-08-01 05:11:05

#13 Re: Help Me ! » finding a circle center using angle in a Semicircle (Thales' Theorem) » 2023-07-30 01:47:48

#14 Help Me ! » How to place Pi in coordinates or line numbers » 2023-07-23 04:37:50

#15 Help Me ! » finding a circle center using angle in a Semicircle (Thales' Theorem) » 2023-07-22 02:00:12

#16 Help Me ! » area of a circle comparing to a sequare! » 2023-07-08 12:13:05

#17 Re: Help Me ! » Calculate a degree of a triangle » 2023-07-03 09:13:14

#18 Re: Help Me ! » Calculate a degree of a triangle » 2023-06-30 01:56:07

#19 Help Me ! » Pairs of angel » 2023-06-30 01:52:32

#20 Re: Help Me ! » Calculate a degree of a triangle » 2023-06-29 22:51:27

#21 Re: Help Me ! » Ratios » 2023-06-29 22:47:42

#22 Help Me ! » Calculate a degree of a triangle » 2023-06-29 22:45:47

#23 Re: Help Me ! » dividing small number over a larger number concept » 2023-06-28 23:34:09

#24 Help Me ! » Ratios » 2023-06-28 06:20:03

#25 Re: Help Me ! » from napier book » 2023-06-28 06:16:17

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