Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step - problem solved #2

This post solves a mathematic problem on Page 32 of the non-fiction book: “Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step”, Andrew Tink, 2018

Problem: An object 2cm, high is held at a distance of 60cm from a convex lens of focal length of 20cm. Find the nature, position, and size of the image.

1. Given:

• Object height (h₁) = 2 cm
• Object distance (u) = -60 cm (negative sign convention)
• Focal length (f) = 20 cm

2. Find Image Distance (v):

• Use the lens formula: 1/f = 1/v - 1/u
• Substitute the given values: 1/20 = 1/v - 1/(-60)
• Simplify: 1/20 = 1/v + 1/60
• 1/v = 1/20 - 1/60
• 1/v = (3 - 1) / 60
• 1/v = 2/60
• v = 60/2
• v = 30 cm

3. Find Image Height (h₂):

• Use the magnification formula: h₂/h₁ = -v/u
• Substitute the values: h₂/2 = -30/(-60)
• h₂/2 = 1/2
• h₂ = 1 cm

4. Determine Nature of Image:

• Since the image distance (v) is positive, the image is real.
• The magnification (h₂/h₁) is positive and less than 1, so the image is inverted and diminished.

Therefore:

• The image is real, inverted, and diminished.
• The image is formed 30 cm from the lens on the opposite side of the object.
• The image height is 1 cm.

Shalom,

Ozhamada

Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step - problem solved #1

This post solves a mathematic problem on Page 32 of the non-fiction book: “Honeysuckle Creek – The story of Tom Reid, A little Dish and Neil Armstrong’s First Step”, Andrew Tink, 2018

Problem: P and Q are points of tangents OP and OQ drawn to a circle whose centre is C; PC and OQ are produced to meet in L; QC and OP are produced to meet in M. Prove that LM is parallel to PQ.

1. Understand the problem:

• We have a circle with centre C.
• OP and OQ are tangents to the circle from an external point O.
• PC is extended to point L.
• QC is extended to point M.
• We need to prove that LM is parallel to PQ.

2. Visualize the problem:

circle with tangents OP and OQ, center C, and points L and M

3. Key concepts:

• Tangents to a circle: A tangent to a circle is a line that touches the circle at exactly one point.
• Radius and tangent: The radius drawn to the point of tangency is perpendicular to the tangent.
• Parallel lines: Two lines are parallel if their corresponding angles are equal.

4. Proof:

• Step 1: Since OP and OQ are tangents to the circle, we know that:
• ∠OPC = 90° (radius perpendicular to tangent)
• ∠OQC = 90° (radius perpendicular to tangent)
• Step 2: Consider triangles OPC and OQC:
• OP = OQ (tangents from an external point to a circle are equal)
• OC is common to both triangles
• ∠OPC = ∠OQC = 90° (proved in step 1)

Therefore, triangles OPC and OQC are congruent by the Hypotenuse-Leg (HL) congruence theorem.

• Step 3: Since triangles OPC and OQC are congruent:
• ∠PCO = ∠QCO (corresponding angles of congruent triangles)
• Step 4: Consider angles ∠PCO and ∠QCM:
• ∠PCO + ∠QCM = 180° (linear pair)

Therefore, ∠QCM = 180° - ∠PCO

• Step 5: Similarly, consider angles ∠QCO and ∠PCM:
• ∠QCO + ∠PCM = 180° (linear pair)

Therefore, ∠PCM = 180° - ∠QCO

• Step 6: Since ∠PCO = ∠QCO (proved in step 3):
• ∠QCM = ∠PCM
• Step 7: In triangles QCM and PCM:
• ∠QCM = ∠PCM (proved in step 6)
• CM is common to both triangles

Therefore, triangles QCM and PCM are congruent by the Angle-Side-Angle (ASA) congruence theorem.

• Step 8: Since triangles QCM and PCM are congruent:
• ∠QMC = ∠PMC (corresponding angles of congruent triangles)
• Step 9: Since ∠QMC = ∠PMC, we can conclude that LM is parallel to PQ (alternate interior angles are equal).

Therefore, we have proved that LM is parallel to PQ.

Shalom,

Ozhamada

Two vehicle-ramming attacks and risk mitigations

It is chilling to return from Christmas leave to learn of two vehicle-ramming attacks. Motor vehicles are a study in risk/reward - they offer us mobility and convenience yet they also can cause carnage. Over Christmas time road and emergency authorities alert the public of the risk of vehicle accidents yet vehicle-ramming attacks highlight the risk that vehicles will be used as weapons.

Timely to the two vehicle-ramming events is a reminder to ensure that risk mitigation measures for public street events include the installation of temporary vehicle barriers. Naturally, there needs to be a balanced measure of implementation of the vehicle barriers in that emergency vehicle access needs to be provided for.

Another risk mitigation measure is to control vehicle movements to scheduled bump-in/bump-out times.

Here is a brief summary of the two vehicle-ramming attacks. I have been cautious in excluding any comment about the rogue actors ethnicity, country of birth or radicalisation, however, it is noteworthy that in both instance the rogue actors had publicly expressed, by social media, in the year prior to the event, intentions to end their lives in a manner that would harm others.

Table 1: Summary of recent vehicle-ramming attacks

Note: A vehicle-ramming attack is an assault in which a perpetrator deliberately rams a vehicle into a building, multiple people, or another vehicle. The count of dead and injured is accurate at 3 January 2025 at the time of publishing this article.

Shalom,

Ozhamada

#NewOrleansAttack

#carattack

#magdeburg

#germany

Children's Christmas Day backyard picnic craft

The brief to young children on a Christmas Day was a paper mâché rendition of an Olympic Swimming Pool. The provided material was a cardboard backing, three sets of coloured A4 paper, a bucket, water, and a net to drain the water as shredded paper was released from the bucket. In addition to the provided material the children artists were invited to pick any items from the garden. 

The results was a three laned pool with four wimmers and two people resting on sun longues. The pool was surrounded by grass.

An excellent effort! And, only three days for it to sun-dry.

To finish it I applied a clear lacquer.

Shalom,

Ozhamada

Kosher crossword 27 August 2024 edition - correction needed

I've copied here an email that I sent to editor@thejewishreport.com.au. The email was available in a monthly Sydney Jewish publication - The Jewish Report - the September 2024 edition - as linked. The images added here are extracted from the publication. Jesus is the answer to the clue: "False god in the Bible"

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Dear Editor,

As a Christian I could put aside the call of my Lord and Saviour and exhibit outrage at the clue and answer to 68 across in the Kosher Crossword of the 27 August 2024 edition; "False god in the Bible". 

Instead, in love, for you and for your readers, I propose you issue a correction in your next edition. The correction would free your readers and allow them to take joy in God's provision circa AD30. The correction would apologise for the false clue and instead offer up an alternative clue: "The second member of the Trinity, God's beloved Son, who bore all the sins of mankind, as revealed in the Gospels". Being culturally sensitive I appreciate that you will wish to publish the corrected clue as: "The second member of the Trinity, G-d's beloved Son, who bore all the sins of mankind, as revealed in the Gospels". 

We Christians see Jesus in the book of Genesis 3 as the offspring who will crush the serpent and Genesis 22 as the ram that is sacrificially offered in our place. In the book of Exodus as the bread of life. In the book of Joshua as the one who will take all into the promised land.

In eager anticipation of the publication of the correction I will pray for you and your readers.

Naturally, I would happily write you an article that identifies Christ in every book of the Old Testament. One Christian preacher has masterfully done just that. See: this Youtube 

from time 17:45 onwards.

Kind regards,

Review of Gentle and Lowly: The Heart of Christ for Sinners and Sufferers

The Bible is symmetric. It opens with the story of a garden (Genesis 1) and closes with a story of a garden (Revelation 22). The reader observes the loss of the initial garden (Genesis 3) and the regaining of a garden (Revelation 21). God is ordered. God loves bookends.

And one hopes that Christian publishing also has ordered bookends.  Gentle and Lowly: The Heart of Christ for Sinners and Sufferers does not have ordered bookends.

The book opens boldly with the opening sentence in the Introduction (copying here the capital letters):

"THIS IS A BOOK ABOUT the heart of Christ" (page 13)

and closes with:

"This is a book about the heart of Christ and of God" (page 225)

The turning point in the book is Chapter 14 (page 127): 

"But our study focuses on the Son of God. What about the Father?"

All-in-all, a fair section of the book is about the Father, so why the bold opening statement? Is it simply an editing error?

---

There were some moments where I found the book uncomfortable:

- Chapter 10 considers a sermon from the year 1740 that Jonathan Edwards presented to children of his church. Ortlund's selective focus upon one part of that sermon - that was one-sixth of the sermon - distracted from the whole message of the sermon. The selectivity suits Ortlund's thesis yet leaves the reader wanting.

- Chapter 17 adds further to the question of what the book is about. That Chapter opens with a statement about what the book is about. Where one has understood from the introduction that the book is about: "the heart of Christ", Chapter 17 advises that "THE MESSAGE OF THIS BOOK is that we tend to project our natural expectations about who God is onto him instead of fighting to let the Bible surprise us into what God himself says".  

And, "fighting" seems to be a very poor choice of word.

- On page 182 there is a puzzle. What exactly is meant by 'to help the gospel'?: 

"Galatians teaches that we are made right with God based on what Christ has done rather than what we do. To help the gospel, therefore, is to lose the gospel" 

Shalom,

Ozhamada

Note: this links from my Goodreads account

A Bible Study; Exodus Chapter 19

 Study 22 June 2024 - Exodus 19

1. Open in prayer

2. Read out loud: Exodus 19:1-2

1. A time to reflect:

1. At what stage is the Exodus journey?

2. What distance are Israelites from the starting point of the journey?

3. What have the Israelites experienced to date? (focus on those events that are of a nation-building nature)

2. Turn to Numbers 1 - which is dated to the same time in history as Exodus 19. How does Numbers 1 help unpack Exodus 18 (that is, how does Numbers 1 show how Moses acted on Jethro’s advice?)

   

   From pexels.com; free and unattributable

   
   

3. Read out loud: Exodus 19:3-13

1. Read Exodus 19:6 together with 1 Peter 2:9: Could it be said that the charge upon Christians is different from the charge upon the Israelites?

2. Exodus 19:9: what assurance may have Moses gained from God’s witness to the people?

3. Exodus 19:10-13: What preparations must the people make? Why are these preparations necessary?

4. Read out loud: Exodus 19:14-24

   

   Image from: https://inspiredscripture.com/bible-studies/exodus-19#gsc.tab=0

1. Describe the morning of the third day - could there have been any doubt of God’s presence?

2. Why is consecration of the people so important (reflect on God’s presence and the purpose of God’s presence as evident of Exodus 20)?

3. What are the roles and responsibilities of Moses and Aaron? (see Zechariah 4:14)

1. How do Moses and Aaron complement each other?

2. How do the roles of Moses and Aaron assist Israel to achieve its objective of a “kingdom of priests”.

3. What other pairings of the roles of Moses and Aaron are evident in the Old Testament?

4. What does Zechariah 4 tell us of what God intended of the roles of King and Priest.

5. Close in prayer