{"0": {"is_chart": [false, false, false], "logo_url": "", "sectionNumber": "", "content_headline_rotations": [], "head_position": {}, "subtitleFontFamily": "", "content_headline_positions": [], "titleFontColor": "", "user_name_rotations": [], "title_position": {}, "logo": "Default", "username_position": {"width": 232.0, "x": -521.0, "y": 330.0, "height": 50.0}, "palette": "Original", "logo_position": "BottomLeft", "description_position": {}, "additional_images": [], "embed_code": ["", "", ""], "images": ["https://online.fliphtml5.com/obtlz/safl/files/large/11e5dc7640969396f45f9a767ea0f428.webp?1732010696", "https://courses.megart.bg/wp-content/uploads/2024/02/%D0%B7%D0%BB%D0%B0%D1%82%D0%BD%D0%BE-%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B59-1-1024x671.jpg", "https://online.fliphtml5.com/obtlz/safl/files/thumb/e4eb8921877bbe931bdaba34e47779e7.webp?1732010696", "https://megavselena.bg/wp-content/uploads/2015/07/Zlatno-sechenie3.png", "https://sinoextrud.com/wp-content/uploads/blue-leather-backpack-with-gold-accents.webp", "https://lookaside.fbsbx.com/lookaside/crawler/media/?media_id=1186780053243916", "https://images.squarespace-cdn.com/content/v1/59b97ff149fc2bf16f7f076d/1565185699232-TBFGKMZSFH0WJOUN7O2Q/%D0%97%D0%BB%D0%B0%D1%82%D0%BD%D0%B8%D1%82%D0%B5%2B%D0%BF%D1%80%D0%BE%D0%BF%D0%BE%D1%80%D1%86%D0%B8%D0%B8.jpg", "https://online.fliphtml5.com/obtlz/safl/files/shot.jpg?1", "https://lookaside.fbsbx.com/lookaside/crawler/media/?media_id=1186780093243912", "https://online.fliphtml5.com/obtlz/safl/files/large/0ab95925ca44251a1e21195304f4045b.webp?1732010696"], "head_rotations": [], "contentFontColor": "", "imageObjectFits": ["cover", "cover", "cover"], "logo_rotation": 0.0, "title_rotations": [], "subtitle": "Your presentation begins here", "media_types": ["image", "image", "image"], "template": "Fun_Education_004", "text_rotations": [], "image_container_positions": [{}, {}, {}], "content_positions": [{}, {}, {}], "background_url": "", "content_rotations": [], "image_container_rotations": [], "logo_numeric_position": {"width": 58.0, "x": -3.0, "y": 586.0, "height": 58.0}, "description": "Description or overview. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nunc et porta ligula. Fusce sodales ipsum quis libero interdum mattis.", "titleFontFamily": "", "title": "", "content": [], "additional_content_indexes": [], "head": "\u0417\u043b\u0430\u0442\u043d\u0438 \u0421\u0435\u0447\u0435\u043d\u0438\u044f", "subtitle_position": {}, "contentHeadlines": [], "subtopic_position": {}, "citations": "", "transcript": "Welcome, everyone! Today, we dive into the fascinating world of the Golden Ratio, a unique number that appears all around us and has inspired artists, architects, and scientists for centuries. We'll explore what it is, where it comes from, and why it matters not just in math but in nature and creativity too. So, get ready to unlock the secrets of this golden mystery together!", "subtitleFontColor": "", "contentFontFamily": "", "subtopic": "", "extra_init_rotations": [], "description_rotations": [], "subtopic_rotations": [], "contentVisualKeywords": [], "userName": "Created using ChatSlide", "isHidden": false, "layout": "ImpactCoverSlide", "sectionNumber_position": {}, "background_color": "", "subtitle_rotations": [], "chart": []}, "1": {"is_chart": [false, false, false], "logo_url": "", "sectionNumber": "", "head_position": {}, "content_headline_rotations": [], "subtitleFontFamily": "", "content_headline_positions": [], "titleFontColor": "", "user_name_rotations": [], "title_position": {}, "username_position": {}, "logo": "Default", "palette": "Original", "logo_position": "BottomLeft", "description_position": {}, "additional_images": [], "embed_code": ["", "", ""], "images": [], "head_rotations": [], "contentFontColor": "", "imageObjectFits": ["cover", "cover", "cover"], "logo_rotation": 0.0, "title_rotations": [], "subtitle": "Your presentation begins here", "media_types": ["image", "image", "image"], "template": "Fun_Education_004", "text_rotations": [], "image_container_positions": [{}, {}, {}], "content_positions": [{"x": -43.0, "y": 482.0}, {}, {}, {"x": 459.0, "width": 200.0, "y": 840.0, "height": 36.0}, {"x": 207.0, "width": 335.0, "y": 88.0, "height": 77.0}], "background_url": "", "logo_numeric_position": {"x": 19.0, "width": 58.0, "y": 636.0, "height": 58.0}, "content_rotations": [], "image_container_rotations": [], "description": "Description or overview. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nunc et porta ligula. Fusce sodales ipsum quis libero interdum mattis.", "titleFontFamily": "", "title": "\u0437\u043b\u0430\u0442\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f", "content": ["

\u041f\u0440\u0435\u043c\u0438\u043d\u0430\u0432\u0430\u043d\u0435 \u043a\u044a\u043c \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435\u0442\u043e

\u0425\u0440\u043e\u043d\u043e\u043b\u043e\u0433\u0438\u044f \u043d\u0430 \u0447\u0430\u0442\u0430

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

is it possible to open the thing to type a code for a presentation on p[ower point

ChatGPT \u043a\u0430\u0437\u0430:

Yes \u2014 it is possible \ud83d\udc4d

It sounds like you\u2019re asking about opening the box where you type a code during a PowerPoint presentation (often for things like live polls, quizzes, or audience interaction).

Here are the common situations and how to open them:

1. If it\u2019s an add-in (Mentimeter, Slido, Poll Everywhere, etc.)

Open your PowerPoint file
Click Slide Show or Insert (depends on the add-in)
Look for the add-in tab (e.g., Mentimeter, Slido)
Click Settings / Connect / Enter Code
The code entry window will pop up

\u27a1\ufe0f During the presentation, the code usually appears automatically when you start Slide Show (F5).

2. If the code is for Presenter View

Start the presentation (F5)
Right-click on the slide
Choose Show Presenter View
The typing/input panel (if used) appears on your screen only

3. If you mean typing while presenting

Press B (black screen) or W (white screen) to pause
Press Esc, type what you need, then restart Slide Show
Or use Presenter View to type without the audience seeing it

4. If nothing appears

Make sure you\u2019re connected to the internet
Check Add-ins are enabled
Try running PowerPoint as full screen (F5)

If you want, tell me what app or tool the code is for (Mentimeter, Slido, Kahoot, etc.), or whether you\u2019re on Windows or Mac, and I\u2019ll give you exact steps.

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

\u0449\u0435 \u0442\u0438 \u043f\u0438\u0448\u0430 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0442\u0435\u043a\u0441\u0442\u0430 \u043f\u0440\u0435\u0432\u0435\u0434\u0438 \u0433\u0438 \u043d\u0430 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438

ChatGPT \u043a\u0430\u0437\u0430:

\u0414\u043e\u0431\u0440\u0435 \ud83d\ude42

\u041f\u0438\u0448\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u0435\u0442\u0435 \u0438 \u0449\u0435 \u0433\u0438 \u043f\u0440\u0435\u0432\u0435\u0434\u0430 \u043d\u0430 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438.

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

oduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

Introduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

ChatGPT \u043c\u043e\u0436\u0435 \u0434\u0430 \u043f\u0440\u0430\u0432\u0438 \u0433\u0440\u0435\u0448\u043a\u0438. \u041f\u0440\u043e\u0432\u0435\u0440\u0435\u0442\u0435 \u0432\u0430\u0436\u043d\u0430\u0442\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f. \u0412\u0438\u0436\u0442\u0435 \u041f\u0440\u0435\u0434\u043f\u043e\u0447\u0438\u0442\u0430\u043d\u0438\u044f \u0437\u0430 \u0431\u0438\u0441\u043a\u0432\u0438\u0442\u043a\u0438\u0442\u0435.

ChatGPT \u043a\u0430\u0437\u0430: **\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435**

", "

\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

", "

\u0412\u0440\u044a\u0437\u043a\u0438 \u0438 \u0438\u0437\u0432\u043e\u0434\u0438

", "

\u041f\u0440\u0435\u043c\u0438\u043d\u0430\u0432\u0430\u043d\u0435 \u043a\u044a\u043c \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435\u0442\u043e

\u0425\u0440\u043e\u043d\u043e\u043b\u043e\u0433\u0438\u044f \u043d\u0430 \u0447\u0430\u0442\u0430

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

is it possible to open the thing to type a code for a presentation on p[ower point

ChatGPT \u043a\u0430\u0437\u0430:

Yes \u2014 it is possible \ud83d\udc4d

It sounds like you\u2019re asking about opening the box where you type a code during a PowerPoint presentation (often for things like live polls, quizzes, or audience interaction).

Here are the common situations and how to open them:

1. If it\u2019s an add-in (Mentimeter, Slido, Poll Everywhere, etc.)

Open your PowerPoint file
Click Slide Show or Insert (depends on the add-in)
Look for the add-in tab (e.g., Mentimeter, Slido)
Click Settings / Connect / Enter Code
The code entry window will pop up

\u27a1\ufe0f During the presentation, the code usually appears automatically when you start Slide Show (F5).

2. If the code is for Presenter View

Start the presentation (F5)
Right-click on the slide
Choose Show Presenter View
The typing/input panel (if used) appears on your screen only

3. If you mean typing while presenting

Press B (black screen) or W (white screen) to pause
Press Esc, type what you need, then restart Slide Show
Or use Presenter View to type without the audience seeing it

4. If nothing appears

Make sure you\u2019re connected to the internet
Check Add-ins are enabled
Try running PowerPoint as full screen (F5)

If you want, tell me what app or tool the code is for (Mentimeter, Slido, Kahoot, etc.), or whether you\u2019re on Windows or Mac, and I\u2019ll give you exact steps.

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

ChatGPT \u043a\u0430\u0437\u0430:

\u0414\u043e\u0431\u0440\u0435 \ud83d\ude42

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

oduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

Introduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

ChatGPT \u043a\u0430\u0437\u0430: **\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435**

", "

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

"], "head": "", "subtitle_position": {}, "additional_content_indexes": [{"type": "text", "value": 3.0}, {"type": "text", "value": 4.0}], "subtopic_position": {}, "contentHeadlines": [], "transcript": "Welcome everyone! Today, we will explore the fascinating topic of the Golden Ratio, or \"\u0437\u043b\u0430\u0442\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f\" as it's known in Bulgarian. Our journey will be divided into three main parts. First, we'll start with an Introduction to the Golden Ratio, understanding what it is, where it comes from, and why it has captured human curiosity for centuries. Next, we will dive into the Applications of the Golden Ratio, discovering how this unique proportion appears in art, architecture, nature, and even technology. Finally, we'll discuss Connections and Insights, where we will reflect on the deeper meanings and relationships the Golden Ratio reveals across various fields. This structure will help us grasp the beauty and significance of the Golden Ratio in a clear and engaging way. So, get ready to uncover the secrets behind one of the most intriguing mathematical concepts that has inspired creativity and wonder throughout history!", "citations": "", "subtitleFontColor": "", "contentFontFamily": "", "subtopic": "

\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435

", "extra_init_rotations": [], "description_rotations": [], "subtopic_rotations": [], "userName": "", "contentVisualKeywords": [], "isHidden": false, "layout": "AgendaSlide", "sectionNumber_position": {}, "background_color": "", "subtitle_rotations": [], "chart": []}, "2": {"is_chart": [false, false, false], "logo_url": "", "sectionNumber": "", "head_position": {}, "content_headline_rotations": [], "subtitleFontFamily": "", "content_headline_positions": [], "titleFontColor": "", "user_name_rotations": [], "title_position": {}, "username_position": {}, "logo": "Default", "palette": "Original", "logo_position": "BottomLeft", "description_position": {}, "additional_images": [], "embed_code": ["", "", ""], "images": [], "head_rotations": [], "contentFontColor": "", "imageObjectFits": ["cover", "cover", "cover"], "logo_rotation": 0.0, "title_rotations": [], "subtitle": "Your presentation begins here", "media_types": ["image", "image", "image"], "template": "Fun_Education_004", "text_rotations": [], "image_container_positions": [{}, {}, {}], "content_positions": [{"x": -43.0, "y": 482.0}, {}, {}, {"x": 459.0, "width": 200.0, "y": 840.0, "height": 36.0}, {"x": 207.0, "width": 335.0, "y": 88.0, "height": 77.0}], "background_url": "", "logo_numeric_position": {"x": 19.0, "width": 58.0, "y": 636.0, "height": 58.0}, "content_rotations": [], "image_container_rotations": [], "description": "Description or overview. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nunc et porta ligula. Fusce sodales ipsum quis libero interdum mattis.", "titleFontFamily": "", "title": "\u0437\u043b\u0430\u0442\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f", "content": ["

\u041f\u0440\u0435\u043c\u0438\u043d\u0430\u0432\u0430\u043d\u0435 \u043a\u044a\u043c \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435\u0442\u043e

\u0425\u0440\u043e\u043d\u043e\u043b\u043e\u0433\u0438\u044f \u043d\u0430 \u0447\u0430\u0442\u0430

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

is it possible to open the thing to type a code for a presentation on p[ower point

ChatGPT \u043a\u0430\u0437\u0430:

Yes \u2014 it is possible \ud83d\udc4d

It sounds like you\u2019re asking about opening the box where you type a code during a PowerPoint presentation (often for things like live polls, quizzes, or audience interaction).

Here are the common situations and how to open them:

1. If it\u2019s an add-in (Mentimeter, Slido, Poll Everywhere, etc.)

Open your PowerPoint file
Click Slide Show or Insert (depends on the add-in)
Look for the add-in tab (e.g., Mentimeter, Slido)
Click Settings / Connect / Enter Code
The code entry window will pop up

\u27a1\ufe0f During the presentation, the code usually appears automatically when you start Slide Show (F5).

2. If the code is for Presenter View

Start the presentation (F5)
Right-click on the slide
Choose Show Presenter View
The typing/input panel (if used) appears on your screen only

3. If you mean typing while presenting

Press B (black screen) or W (white screen) to pause
Press Esc, type what you need, then restart Slide Show
Or use Presenter View to type without the audience seeing it

4. If nothing appears

Make sure you\u2019re connected to the internet
Check Add-ins are enabled
Try running PowerPoint as full screen (F5)

If you want, tell me what app or tool the code is for (Mentimeter, Slido, Kahoot, etc.), or whether you\u2019re on Windows or Mac, and I\u2019ll give you exact steps.

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

ChatGPT \u043a\u0430\u0437\u0430:

\u0414\u043e\u0431\u0440\u0435 \ud83d\ude42

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

oduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

Introduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

ChatGPT \u043a\u0430\u0437\u0430: **\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435**

", "

\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

", "

\u0412\u0440\u044a\u0437\u043a\u0438 \u0438 \u0438\u0437\u0432\u043e\u0434\u0438

", "

\u041f\u0440\u0435\u043c\u0438\u043d\u0430\u0432\u0430\u043d\u0435 \u043a\u044a\u043c \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435\u0442\u043e

\u0425\u0440\u043e\u043d\u043e\u043b\u043e\u0433\u0438\u044f \u043d\u0430 \u0447\u0430\u0442\u0430

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

is it possible to open the thing to type a code for a presentation on p[ower point

ChatGPT \u043a\u0430\u0437\u0430:

Yes \u2014 it is possible \ud83d\udc4d

It sounds like you\u2019re asking about opening the box where you type a code during a PowerPoint presentation (often for things like live polls, quizzes, or audience interaction).

Here are the common situations and how to open them:

1. If it\u2019s an add-in (Mentimeter, Slido, Poll Everywhere, etc.)

Open your PowerPoint file
Click Slide Show or Insert (depends on the add-in)
Look for the add-in tab (e.g., Mentimeter, Slido)
Click Settings / Connect / Enter Code
The code entry window will pop up

\u27a1\ufe0f During the presentation, the code usually appears automatically when you start Slide Show (F5).

2. If the code is for Presenter View

Start the presentation (F5)
Right-click on the slide
Choose Show Presenter View
The typing/input panel (if used) appears on your screen only

3. If you mean typing while presenting

Press B (black screen) or W (white screen) to pause
Press Esc, type what you need, then restart Slide Show
Or use Presenter View to type without the audience seeing it

4. If nothing appears

Make sure you\u2019re connected to the internet
Check Add-ins are enabled
Try running PowerPoint as full screen (F5)

If you want, tell me what app or tool the code is for (Mentimeter, Slido, Kahoot, etc.), or whether you\u2019re on Windows or Mac, and I\u2019ll give you exact steps.

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

ChatGPT \u043a\u0430\u0437\u0430:

\u0414\u043e\u0431\u0440\u0435 \ud83d\ude42

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

oduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

\u0412\u0438\u0435 \u043a\u0430\u0437\u0430\u0445\u0442\u0435:

Introduction to the Golden Ratio

ChatGPT \u043a\u0430\u0437\u0430:

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

ChatGPT \u043a\u0430\u0437\u0430: **\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435**

", "

\u0412\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435

\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435

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\u0417\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u043d\u043e 1,618, \u0435 \u0438\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0447\u0438\u0441\u043b\u043e, \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0432\u0430\u043d\u043e \u0441 \u0444\u0438 (\u03c6), \u043a\u043e\u0435\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430 \u0443\u043d\u0438\u043a\u0430\u043b\u043d\u043e\u0442\u043e \u0441\u044a\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435, \u043f\u0440\u0438 \u043a\u043e\u0435\u0442\u043e

((a + b) / a = a / b).

", "

\u0428\u0438\u0440\u043e\u043a\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u0442\u043e \u0437\u0430 \u0441\u0432\u043e\u0438\u0442\u0435 \u043f\u0440\u0438\u044f\u0442\u043d\u0438 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u0438, \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u0432 \u0438\u0437\u043a\u0443\u0441\u0442\u0432\u043e\u0442\u043e, \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430\u0442\u0430 \u0438 \u0434\u0438\u0437\u0430\u0439\u043d\u0430 \u0437\u0430 \u043f\u043e\u0441\u0442\u0438\u0433\u0430\u043d\u0435 \u043d\u0430 \u0445\u0430\u0440\u043c\u043e\u043d\u0438\u044f \u0438 \u0431\u0430\u043b\u0430\u043d\u0441.

", "

\u0420\u0430\u0437\u0431\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0432\u0430 \u0441\u044a\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u043e\u0434\u043f\u043e\u043c\u0430\u0433\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u0443\u0441\u0432\u043e\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u0442\u0430, \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u0438\u0442\u0435 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u0432 \u0440\u0435\u0430\u043b\u043d\u0438\u044f \u0441\u0432\u044f\u0442.

", "Technical analysts sometimes apply Fibonacci retracements based on the Golden Ratio to forecast stock price movements (Investopedia, 2023)."], "head": "", "subtitle_position": {}, "additional_content_indexes": [], "subtopic_position": {}, "contentHeadlines": ["

\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435

", "

\u0415\u0441\u0442\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435

", "

\u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0437\u043d\u0430\u0447\u0438\u043c\u043e\u0441\u0442

", "Applications in Finance"], "transcript": "The Golden Ratio, often represented by the Greek letter phi (\u03c6), is approximately 1.618. It defines a unique proportion where the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller. This remarkable number appears repeatedly in nature, from the spirals of shells to branching patterns in trees, captivating observers with its inherent harmony and balance. Historically, it has fascinated mathematicians, artists, and architects alike, becoming a symbol of aesthetic perfection across centuries.", "citations": [], "subtitleFontColor": "", "contentFontFamily": "", "subtopic": "

\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435

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\u0417\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 \u0435 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u043e \u0432 \u0414\u0440\u0435\u0432\u043d\u0430 \u0413\u044a\u0440\u0446\u0438\u044f \u043e\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438 \u043a\u0430\u0442\u043e \u0415\u0432\u043a\u043b\u0438\u0434, \u043a\u043e\u0439\u0442\u043e \u0433\u043e \u043e\u043f\u0438\u0441\u0432\u0430 \u0432 \u0441\u0432\u043e\u044f \u0442\u0440\u0443\u0434 \u201e\u0415\u043b\u0435\u043c\u0435\u043d\u0442\u0438\u201c \u043e\u043a\u043e\u043b\u043e 300 \u0433. \u043f\u0440.\u043d.\u0435.

", "

\u0425\u0443\u0434\u043e\u0436\u043d\u0438\u0446\u0438 \u043a\u0430\u0442\u043e \u041b\u0435\u043e\u043d\u0430\u0440\u0434\u043e \u0434\u0430 \u0412\u0438\u043d\u0447\u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043b\u0438 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 \u0437\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0431\u0430\u043b\u0430\u043d\u0441\u0438\u0440\u0430\u043d\u0438 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0438 \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u043d\u0438 \u0434\u0438\u0437\u0430\u0439\u043d\u0438.

", "

\u0421\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0438\u0442\u0435 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0438\u044f \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u0442 \u0432\u0440\u044a\u0437\u043a\u0438\u0442\u0435 \u043d\u0430 \u0444\u0438 (\u03c6) \u0441 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u0438, \u0442\u0435\u043e\u0440\u0438\u044f \u043d\u0430 \u0445\u0430\u043e\u0441\u0430 \u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0442\u0435 \u043d\u0430 \u0440\u0430\u0441\u0442\u0435\u0436 \u0432 \u043f\u0440\u0438\u0440\u043e\u0434\u0430\u0442\u0430.

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\u0414\u0440\u0435\u0432\u043d\u0438 \u043f\u0440\u043e\u0438\u0437\u0445\u043e\u0434\u0438

", "

\u0418\u0437\u043a\u0443\u0441\u0442\u0432\u043e \u0438 \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u043e\u0442 \u0420\u0435\u043d\u0435\u0441\u0430\u043d\u0441\u0430

", "

\u041c\u043e\u0434\u0435\u0440\u0435\u043d \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0438\u043d\u0442\u0435\u0440\u0435\u0441

"], "transcript": "The Golden Ratio, often symbolized by the Greek letter phi, approximately equal to 1.618, is a unique mathematical relationship that has fascinated scholars for centuries. It first gained formal attention in Ancient Greece, with Euclid describing it in his work 'Elements' around 300 BCE. You can observe this ratio in nature\u2014from the spirals of shells to the pattern of sunflower seeds\u2014showing how mathematics manifests beautifully in the natural world. Understanding its historical roots enriches our appreciation of how this ratio connects art, nature, and science across time.", "citations": [], "subtitleFontColor": "", "contentFontFamily": "", "subtopic": "

\u0418\u0441\u0442\u043e\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0435\u0433\u043b\u0435\u0434

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\u0424\u0438\u043b\u043e\u0442\u0430\u043a\u0441\u0438\u0441\u044a\u0442, \u043f\u043e\u0434\u0440\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043b\u0438\u0441\u0442\u0430\u0442\u0430 \u0438 \u0441\u0435\u043c\u0435\u043d\u0430\u0442\u0430, \u0447\u0435\u0441\u0442\u043e \u0441\u043b\u0435\u0434\u0432\u0430 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435, \u043a\u0430\u0442\u043e \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0438\u0440\u0430 \u0443\u0441\u0432\u043e\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0441\u043b\u044a\u043d\u0447\u0435\u0432\u0430 \u0441\u0432\u0435\u0442\u043b\u0438\u043d\u0430 \u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e\u0442\u043e (Journal of Botany, 2021).

", "

\u0421\u043f\u0438\u0440\u0430\u043b\u043d\u0438\u0442\u0435 \u0447\u0435\u0440\u0443\u043f\u043a\u0438 \u0438 \u0434\u043e\u0440\u0438 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u0438\u0442\u0435 \u0432 \u0442\u0435\u043b\u0430\u0442\u0430 \u043d\u0430 \u0436\u0438\u0432\u043e\u0442\u043d\u0438\u0442\u0435 \u043f\u043e\u043a\u0430\u0437\u0432\u0430\u0442 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438, \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0438 \u043d\u0430 \u0444\u0438 (\u03c6).

", "

\u041f\u0430\u0437\u0430\u0440\u043d\u0438\u0442\u0435 \u0438\u043d\u0434\u0435\u043a\u0441\u0438 \u043f\u043e\u043d\u044f\u043a\u043e\u0433\u0430 \u043f\u043e\u043a\u0430\u0437\u0432\u0430\u0442 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0438, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441\u044a\u0441 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435, \u0432 \u0446\u0438\u043a\u043b\u0438\u0447\u043d\u0438\u0442\u0435 \u0441\u0438 \u0442\u0435\u043d\u0434\u0435\u043d\u0446\u0438\u0438 (Bloomberg Finance Data).

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\u0414\u043e\u043a\u043b\u0430\u0434 \u043e\u0442 2022 \u0433. \u043f\u043e\u043a\u0430\u0437\u0432\u0430 38% \u043f\u043e-\u0432\u0438\u0441\u043e\u043a\u0430 \u0430\u043d\u0433\u0430\u0436\u0438\u0440\u0430\u043d\u043e\u0441\u0442 \u043d\u0430 \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0442\u0430 \u043f\u0440\u0438 \u043c\u0430\u0440\u043a\u0435\u0442\u0438\u043d\u0433\u043e\u0432\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438, \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0449\u0438 \u043e\u0444\u043e\u0440\u043c\u043b\u0435\u043d\u0438\u044f, \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0437\u043b\u0430\u0442\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 (Design Trends Magazine, 2022).

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