#futotop — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #futotop, aggregated by home.social.
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“The Three Identities — Technology, Geography, and Mathematics”
If there were a biography about you, what would the title be? Overview The biography about me would be titled the name of the title of this post, representing the Three Identities I own and create—novaTopFlex, geoTopFlex, and futoTopFlex. Apart from the Three Identities as an abstract, I have also incorporated elements from the Three Identities located elsewhere, such as the technology industry, geography topics, and the remaining pillars of cultural interest—mathematics, science, fine […] -
Hype for the Future 103D → Returning to novaTopFlex
Introduction On this Wednesday, February 11, 2026, the Three Identities of novaTopFlex, geoTopFlex, and futoTopFlex are each associated with distinctive identities, with predominantly geoTopFlex content having been featured thus far. Rules for the Three Identities include rules of consent (which are always to be top priority), as well as rules on personal and extreme responsibility. While the vast majority of the February content for novaTopFlex has been under the theme of geography, […] -
Hype for the Future 103D → Returning to novaTopFlex
Introduction On this Wednesday, February 11, 2026, the Three Identities of novaTopFlex, geoTopFlex, and futoTopFlex are each associated with distinctive identities, with predominantly geoTopFlex content having been featured thus far. Rules for the Three Identities include rules of consent (which are always to be top priority), as well as rules on personal and extreme responsibility. While the vast majority of the February content for novaTopFlex has been under the theme of geography, […] -
Hype for the Future 103D → Returning to novaTopFlex
Introduction On this Wednesday, February 11, 2026, the Three Identities of novaTopFlex, geoTopFlex, and futoTopFlex are each associated with distinctive identities, with predominantly geoTopFlex content having been featured thus far. Rules for the Three Identities include rules of consent (which are always to be top priority), as well as rules on personal and extreme responsibility. While the vast majority of the February content for novaTopFlex has been under the theme of geography, […] -
Hype for the Future 103D → Returning to novaTopFlex
Introduction On this Wednesday, February 11, 2026, the Three Identities of novaTopFlex, geoTopFlex, and futoTopFlex are each associated with distinctive identities, with predominantly geoTopFlex content having been featured thus far. Rules for the Three Identities include rules of consent (which are always to be top priority), as well as rules on personal and extreme responsibility. While the vast majority of the February content for novaTopFlex has been under the theme of geography, […] -
Hype for the Future 103D → Returning to novaTopFlex
Introduction On this Wednesday, February 11, 2026, the Three Identities of novaTopFlex, geoTopFlex, and futoTopFlex are each associated with distinctive identities, with predominantly geoTopFlex content having been featured thus far. Rules for the Three Identities include rules of consent (which are always to be top priority), as well as rules on personal and extreme responsibility. While the vast majority of the February content for novaTopFlex has been under the theme of geography, […] -
Hype for the Future 42A: More about BosWash
The Northeast Megalopolis is largely determined by Boston, New York, Philadelphia, Baltimore, and Washington. However, additional smaller cities also play a role in the BosWash corridor, sometimes suburban, sometimes satellite cities, other times by way of being independent in their own right. Occasionally included are northern and southern extensions of the Northeast Megalopolis to cover Portsmouth, Portland, and Bangor to the north; and Richmond and Hampton Roads to the south. Regardless of […]https://novatopflex.wordpress.com/2025/12/12/hype-for-the-future-42a-more-about-boswash/
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Hype for the Future 42A: More about BosWash
The Northeast Megalopolis is largely determined by Boston, New York, Philadelphia, Baltimore, and Washington. However, additional smaller cities also play a role in the BosWash corridor, sometimes suburban, sometimes satellite cities, other times by way of being independent in their own right. Occasionally included are northern and southern extensions of the Northeast Megalopolis to cover Portsmouth, Portland, and Bangor to the north; and Richmond and Hampton Roads to the south. Regardless of […]https://novatopflex.wordpress.com/2025/12/12/hype-for-the-future-42a-more-about-boswash/
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Hype for the Future 42A: More about BosWash
The Northeast Megalopolis is largely determined by Boston, New York, Philadelphia, Baltimore, and Washington. However, additional smaller cities also play a role in the BosWash corridor, sometimes suburban, sometimes satellite cities, other times by way of being independent in their own right. Occasionally included are northern and southern extensions of the Northeast Megalopolis to cover Portsmouth, Portland, and Bangor to the north; and Richmond and Hampton Roads to the south. Regardless of […]https://novatopflex.wordpress.com/2025/12/12/hype-for-the-future-42a-more-about-boswash/
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Hype for the Future 42A: More about BosWash
The Northeast Megalopolis is largely determined by Boston, New York, Philadelphia, Baltimore, and Washington. However, additional smaller cities also play a role in the BosWash corridor, sometimes suburban, sometimes satellite cities, other times by way of being independent in their own right. Occasionally included are northern and southern extensions of the Northeast Megalopolis to cover Portsmouth, Portland, and Bangor to the north; and Richmond and Hampton Roads to the south. Regardless of […]https://novatopflex.wordpress.com/2025/12/12/hype-for-the-future-42a-more-about-boswash/
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Hype for the Future 42A: More about BosWash
The Northeast Megalopolis is largely determined by Boston, New York, Philadelphia, Baltimore, and Washington. However, additional smaller cities also play a role in the BosWash corridor, sometimes suburban, sometimes satellite cities, other times by way of being independent in their own right. Occasionally included are northern and southern extensions of the Northeast Megalopolis to cover Portsmouth, Portland, and Bangor to the north; and Richmond and Hampton Roads to the south. Regardless of […]https://novatopflex.wordpress.com/2025/12/12/hype-for-the-future-42a-more-about-boswash/
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Hype for the Future 31/284: Snow until January 4th
Today is Monday, December 1st, 2025! On this day, select WordPress sites can display falling snow for the first time since early January, 2025. The falling snow session occurs for five weeks, ending on Sunday, January 4th, 2026.
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Hype for the Future 18D: Why Columbus over Cincinnati?
Fear of judgment at numerous social events is often multifaceted, dependent on the event, event type, event duration, event location, and additional factors. Within Columbus, however, is an environment that dispels the fear of judgment through the citywide promotion of modern--even postmodern--values and cultural ethics. Therefore, novaTopFlex shall focus on and prioritize Columbus-area opportunities and prize such opportunities above Cincinnati-area opportunities, particularly as Columbus is […]https://novatopflex.wordpress.com/2025/11/18/hype-for-the-future-18d-why-columbus-over-cincinnati/
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Hype for the Future 18D: Why Columbus over Cincinnati?
Fear of judgment at numerous social events is often multifaceted, dependent on the event, event type, event duration, event location, and additional factors. Within Columbus, however, is an environment that dispels the fear of judgment through the citywide promotion of modern--even postmodern--values and cultural ethics. Therefore, novaTopFlex shall focus on and prioritize Columbus-area opportunities and prize such opportunities above Cincinnati-area opportunities, particularly as Columbus is […]https://novatopflex.wordpress.com/2025/11/18/hype-for-the-future-18d-why-columbus-over-cincinnati/
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Hype for the Future 18D: Why Columbus over Cincinnati?
Fear of judgment at numerous social events is often multifaceted, dependent on the event, event type, event duration, event location, and additional factors. Within Columbus, however, is an environment that dispels the fear of judgment through the citywide promotion of modern--even postmodern--values and cultural ethics. Therefore, novaTopFlex shall focus on and prioritize Columbus-area opportunities and prize such opportunities above Cincinnati-area opportunities, particularly as Columbus is […]https://novatopflex.wordpress.com/2025/11/18/hype-for-the-future-18d-why-columbus-over-cincinnati/
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Hype for the Future 18D: Why Columbus over Cincinnati?
Fear of judgment at numerous social events is often multifaceted, dependent on the event, event type, event duration, event location, and additional factors. Within Columbus, however, is an environment that dispels the fear of judgment through the citywide promotion of modern--even postmodern--values and cultural ethics. Therefore, novaTopFlex shall focus on and prioritize Columbus-area opportunities and prize such opportunities above Cincinnati-area opportunities, particularly as Columbus is […]https://novatopflex.wordpress.com/2025/11/18/hype-for-the-future-18d-why-columbus-over-cincinnati/
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Hype for the Future 18D: Why Columbus over Cincinnati?
Fear of judgment at numerous social events is often multifaceted, dependent on the event, event type, event duration, event location, and additional factors. Within Columbus, however, is an environment that dispels the fear of judgment through the citywide promotion of modern--even postmodern--values and cultural ethics. Therefore, novaTopFlex shall focus on and prioritize Columbus-area opportunities and prize such opportunities above Cincinnati-area opportunities, particularly as Columbus is […]https://novatopflex.wordpress.com/2025/11/18/hype-for-the-future-18d-why-columbus-over-cincinnati/
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Hype for the Future 18C: Notable Quirks of the novaTop Identity
With the creativity and desire for freedom of identity and expression and the deconstruction of stereotypes and forced conformity, as well as natural talent for art and music existing within the novaTop, geoTop, and futoTop communities, novaTopFlex is absolutely interested in the existing cultural arts scenes. novaTopFlex transforms from a computer scientist...to a computer programmer...to a cybersecurity enthusiast...to a technology expert...to a geography master...to a cultural hub...to a […] -
Hype for the Future 18C: Notable Quirks of the novaTop Identity
With the creativity and desire for freedom of identity and expression and the deconstruction of stereotypes and forced conformity, as well as natural talent for art and music existing within the novaTop, geoTop, and futoTop communities, novaTopFlex is absolutely interested in the existing cultural arts scenes. novaTopFlex transforms from a computer scientist...to a computer programmer...to a cybersecurity enthusiast...to a technology expert...to a geography master...to a cultural hub...to a […] -
Hype for the Future 18C: Notable Quirks of the novaTop Identity
With the creativity and desire for freedom of identity and expression and the deconstruction of stereotypes and forced conformity, as well as natural talent for art and music existing within the novaTop, geoTop, and futoTop communities, novaTopFlex is absolutely interested in the existing cultural arts scenes. novaTopFlex transforms from a computer scientist...to a computer programmer...to a cybersecurity enthusiast...to a technology expert...to a geography master...to a cultural hub...to a […] -
Hype for the Future 18C: Notable Quirks of the novaTop Identity
With the creativity and desire for freedom of identity and expression and the deconstruction of stereotypes and forced conformity, as well as natural talent for art and music existing within the novaTop, geoTop, and futoTop communities, novaTopFlex is absolutely interested in the existing cultural arts scenes. novaTopFlex transforms from a computer scientist...to a computer programmer...to a cybersecurity enthusiast...to a technology expert...to a geography master...to a cultural hub...to a […] -
Hype for the Future 18C: Notable Quirks of the novaTop Identity
With the creativity and desire for freedom of identity and expression and the deconstruction of stereotypes and forced conformity, as well as natural talent for art and music existing within the novaTop, geoTop, and futoTop communities, novaTopFlex is absolutely interested in the existing cultural arts scenes. novaTopFlex transforms from a computer scientist...to a computer programmer...to a cybersecurity enthusiast...to a technology expert...to a geography master...to a cultural hub...to a […] -
Hype for the Future 18B: The Official Identity of novaTopFlex in Massachusetts
novaTopFlex shall celebrate the birthday of Susan B. Anthony on February 15 every year, as she was first born on that day in 1820. Per the "Hype for the Future" convention, which started the schedule with November 1, Anthony's birthday is Hype for the Future 107. Susan B. Anthony had most notably lived within Adams, Massachusetts; and Battenville, Canajoharie, and Rochester, New York. Although she was born within the Town of Adams, Berkshire County, Massachusetts, her family would move to the […] -
Hype for the Future 18B: The Official Identity of novaTopFlex in Massachusetts
novaTopFlex shall celebrate the birthday of Susan B. Anthony on February 15 every year, as she was first born on that day in 1820. Per the "Hype for the Future" convention, which started the schedule with November 1, Anthony's birthday is Hype for the Future 107. Susan B. Anthony had most notably lived within Adams, Massachusetts; and Battenville, Canajoharie, and Rochester, New York. Although she was born within the Town of Adams, Berkshire County, Massachusetts, her family would move to the […] -
Hype for the Future 18B: The Official Identity of novaTopFlex in Massachusetts
novaTopFlex shall celebrate the birthday of Susan B. Anthony on February 15 every year, as she was first born on that day in 1820. Per the "Hype for the Future" convention, which started the schedule with November 1, Anthony's birthday is Hype for the Future 107. Susan B. Anthony had most notably lived within Adams, Massachusetts; and Battenville, Canajoharie, and Rochester, New York. Although she was born within the Town of Adams, Berkshire County, Massachusetts, her family would move to the […] -
Hype for the Future 18B: The Official Identity of novaTopFlex in Massachusetts
novaTopFlex shall celebrate the birthday of Susan B. Anthony on February 15 every year, as she was first born on that day in 1820. Per the "Hype for the Future" convention, which started the schedule with November 1, Anthony's birthday is Hype for the Future 107. Susan B. Anthony had most notably lived within Adams, Massachusetts; and Battenville, Canajoharie, and Rochester, New York. Although she was born within the Town of Adams, Berkshire County, Massachusetts, her family would move to the […] -
Hype for the Future 9C: Expanding Horizons
While novaTopFlex has initially been associated with New England, New York, and the Great Lakes region, the Mid-Atlantic and Lower Midwest regions have become particularly interesting under very similar circumstances. Even further south, novaTopFlex is increasingly interested in pursuing appropriate opportunities into the Tidewater region and the Upland South in particular. Apart from southward, novaTopFlex is also pursuing expansion westward, particularly into Nebraska and Kansas (North […]https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9c-expanding-horizons/
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Hype for the Future 9C: Expanding Horizons
While novaTopFlex has initially been associated with New England, New York, and the Great Lakes region, the Mid-Atlantic and Lower Midwest regions have become particularly interesting under very similar circumstances. Even further south, novaTopFlex is increasingly interested in pursuing appropriate opportunities into the Tidewater region and the Upland South in particular. Apart from southward, novaTopFlex is also pursuing expansion westward, particularly into Nebraska and Kansas (North […]https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9c-expanding-horizons/
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Hype for the Future 9C: Expanding Horizons
While novaTopFlex has initially been associated with New England, New York, and the Great Lakes region, the Mid-Atlantic and Lower Midwest regions have become particularly interesting under very similar circumstances. Even further south, novaTopFlex is increasingly interested in pursuing appropriate opportunities into the Tidewater region and the Upland South in particular. Apart from southward, novaTopFlex is also pursuing expansion westward, particularly into Nebraska and Kansas (North […]https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9c-expanding-horizons/
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Hype for the Future 9C: Expanding Horizons
While novaTopFlex has initially been associated with New England, New York, and the Great Lakes region, the Mid-Atlantic and Lower Midwest regions have become particularly interesting under very similar circumstances. Even further south, novaTopFlex is increasingly interested in pursuing appropriate opportunities into the Tidewater region and the Upland South in particular. Apart from southward, novaTopFlex is also pursuing expansion westward, particularly into Nebraska and Kansas (North […]https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9c-expanding-horizons/
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Hype for the Future 9C: Expanding Horizons
While novaTopFlex has initially been associated with New England, New York, and the Great Lakes region, the Mid-Atlantic and Lower Midwest regions have become particularly interesting under very similar circumstances. Even further south, novaTopFlex is increasingly interested in pursuing appropriate opportunities into the Tidewater region and the Upland South in particular. Apart from southward, novaTopFlex is also pursuing expansion westward, particularly into Nebraska and Kansas (North […]https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9c-expanding-horizons/
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Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
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Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
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Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
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Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
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Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
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Hype for the Future 9/284: How to Connect with the novaTop Identity from Afar
While novaTopFlex may be the launcher of philosophical debates and a carrier of values beyond traditions, the novaTop community is also an essential community to function in identifying new beliefs in social roles. Insofar as the novaTopFlex community has identified, such beliefs and belief systems have included, but may not have been limited to, beliefs shared primarily with communities in Vermont, New York, and Western Massachusetts (the Berkshires, Pioneer Valley, and the west side of […] -
Hype for the Future 9/284: How to Connect with the novaTop Identity from Afar
While novaTopFlex may be the launcher of philosophical debates and a carrier of values beyond traditions, the novaTop community is also an essential community to function in identifying new beliefs in social roles. Insofar as the novaTopFlex community has identified, such beliefs and belief systems have included, but may not have been limited to, beliefs shared primarily with communities in Vermont, New York, and Western Massachusetts (the Berkshires, Pioneer Valley, and the west side of […] -
Hype for the Future 9/284: How to Connect with the novaTop Identity from Afar
While novaTopFlex may be the launcher of philosophical debates and a carrier of values beyond traditions, the novaTop community is also an essential community to function in identifying new beliefs in social roles. Insofar as the novaTopFlex community has identified, such beliefs and belief systems have included, but may not have been limited to, beliefs shared primarily with communities in Vermont, New York, and Western Massachusetts (the Berkshires, Pioneer Valley, and the west side of […] -
Hype for the Future 9/284: How to Connect with the novaTop Identity from Afar
While novaTopFlex may be the launcher of philosophical debates and a carrier of values beyond traditions, the novaTop community is also an essential community to function in identifying new beliefs in social roles. Insofar as the novaTopFlex community has identified, such beliefs and belief systems have included, but may not have been limited to, beliefs shared primarily with communities in Vermont, New York, and Western Massachusetts (the Berkshires, Pioneer Valley, and the west side of […] -
Hype for the Future 9/284: How to Connect with the novaTop Identity from Afar
While novaTopFlex may be the launcher of philosophical debates and a carrier of values beyond traditions, the novaTop community is also an essential community to function in identifying new beliefs in social roles. Insofar as the novaTopFlex community has identified, such beliefs and belief systems have included, but may not have been limited to, beliefs shared primarily with communities in Vermont, New York, and Western Massachusetts (the Berkshires, Pioneer Valley, and the west side of […] -
Hype for the Future 8A: The novaTop Travel Itinerary Goals
Over the next several months, novaTopFlex shall ideally take on mathematics pursuits, but also the occasional concert-style events at Bogart’s, Brady, and Riverbend; plus artistic joy and expression throughout the time. Apart from the aforementioned ideal goals, novaTopFlex shall also ideally take on the events in Lebanon, Ohio, including the horse-drawn carriage rides and country and jazz music festivals. Furthermore, novaTopFlex shall ideally also take on pursuits of balloon rides, […] -
Hype for the Future 8A: The novaTop Travel Itinerary Goals
Over the next several months, novaTopFlex shall ideally take on mathematics pursuits, but also the occasional concert-style events at Bogart’s, Brady, and Riverbend; plus artistic joy and expression throughout the time. Apart from the aforementioned ideal goals, novaTopFlex shall also ideally take on the events in Lebanon, Ohio, including the horse-drawn carriage rides and country and jazz music festivals. Furthermore, novaTopFlex shall ideally also take on pursuits of balloon rides, […] -
Hype for the Future 8A: The novaTop Travel Itinerary Goals
Over the next several months, novaTopFlex shall ideally take on mathematics pursuits, but also the occasional concert-style events at Bogart’s, Brady, and Riverbend; plus artistic joy and expression throughout the time. Apart from the aforementioned ideal goals, novaTopFlex shall also ideally take on the events in Lebanon, Ohio, including the horse-drawn carriage rides and country and jazz music festivals. Furthermore, novaTopFlex shall ideally also take on pursuits of balloon rides, […] -
Hype for the Future 8A: The novaTop Travel Itinerary Goals
Over the next several months, novaTopFlex shall ideally take on mathematics pursuits, but also the occasional concert-style events at Bogart’s, Brady, and Riverbend; plus artistic joy and expression throughout the time. Apart from the aforementioned ideal goals, novaTopFlex shall also ideally take on the events in Lebanon, Ohio, including the horse-drawn carriage rides and country and jazz music festivals. Furthermore, novaTopFlex shall ideally also take on pursuits of balloon rides, […] -
Hype for the Future 8A: The novaTop Travel Itinerary Goals
Over the next several months, novaTopFlex shall ideally take on mathematics pursuits, but also the occasional concert-style events at Bogart’s, Brady, and Riverbend; plus artistic joy and expression throughout the time. Apart from the aforementioned ideal goals, novaTopFlex shall also ideally take on the events in Lebanon, Ohio, including the horse-drawn carriage rides and country and jazz music festivals. Furthermore, novaTopFlex shall ideally also take on pursuits of balloon rides, […] -
Hype for the Future 7A: Mathematics Edition
The hyperbolic functions of the sine and of the cosine are identified as follows:
sinh(x)=(e^x-e^(-x))/2
cosh(x)=(e^x+e^(-x))/2
The remaining hyperbolic trigonometric functions can be constructed with the hyperbolic versions of the appropriate functions. While tan(x)=sin(x)/cos(x), tanh(x)=sinh(x)/cosh(x) and can be constructed as (e^x-e^(-x))/(e^x+e^(-x)).
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Hype for the Future 7A: Mathematics Edition
The hyperbolic functions of the sine and of the cosine are identified as follows:
sinh(x)=(e^x-e^(-x))/2
cosh(x)=(e^x+e^(-x))/2
The remaining hyperbolic trigonometric functions can be constructed with the hyperbolic versions of the appropriate functions. While tan(x)=sin(x)/cos(x), tanh(x)=sinh(x)/cosh(x) and can be constructed as (e^x-e^(-x))/(e^x+e^(-x)).
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Hype for the Future 7A: Mathematics Edition
The hyperbolic functions of the sine and of the cosine are identified as follows:
sinh(x)=(e^x-e^(-x))/2
cosh(x)=(e^x+e^(-x))/2
The remaining hyperbolic trigonometric functions can be constructed with the hyperbolic versions of the appropriate functions. While tan(x)=sin(x)/cos(x), tanh(x)=sinh(x)/cosh(x) and can be constructed as (e^x-e^(-x))/(e^x+e^(-x)).
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Hype for the Future 7A: Mathematics Edition
The hyperbolic functions of the sine and of the cosine are identified as follows:
sinh(x)=(e^x-e^(-x))/2
cosh(x)=(e^x+e^(-x))/2
The remaining hyperbolic trigonometric functions can be constructed with the hyperbolic versions of the appropriate functions. While tan(x)=sin(x)/cos(x), tanh(x)=sinh(x)/cosh(x) and can be constructed as (e^x-e^(-x))/(e^x+e^(-x)).