Are there any other shorter expressions for 8 by manipulating exactly 4 4?












1












$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    14 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    13 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 mins ago
















1












$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    14 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    13 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 mins ago














1












1








1





$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$




The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions




integer-partitions






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 18 mins ago









Artificial StupidityArtificial Stupidity

353110




353110








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    14 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    13 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 mins ago














  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    14 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    13 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 mins ago








2




2




$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
14 mins ago




$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
14 mins ago












$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
13 mins ago




$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
13 mins ago












$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
10 mins ago




$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
10 mins ago










3 Answers
3






active

oldest

votes


















2












$begingroup$

Here is one: $frac{4times4}4+4=8$



Here is another one: $frac{4!}{4-frac44}=8$






share|cite|improve this answer









$endgroup$





















    2












    $begingroup$

    Here my ones: :-)




    • $(4+4)cdotfrac{4}{4}$

    • $4cdot sqrt[4]{4cdot 4}$






    share|cite









    $endgroup$













    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      5 mins ago



















    1












    $begingroup$

    We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



    Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






    share|cite|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3089195%2fare-there-any-other-shorter-expressions-for-8-by-manipulating-exactly-4-4%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      Here is one: $frac{4times4}4+4=8$



      Here is another one: $frac{4!}{4-frac44}=8$






      share|cite|improve this answer









      $endgroup$


















        2












        $begingroup$

        Here is one: $frac{4times4}4+4=8$



        Here is another one: $frac{4!}{4-frac44}=8$






        share|cite|improve this answer









        $endgroup$
















          2












          2








          2





          $begingroup$

          Here is one: $frac{4times4}4+4=8$



          Here is another one: $frac{4!}{4-frac44}=8$






          share|cite|improve this answer









          $endgroup$



          Here is one: $frac{4times4}4+4=8$



          Here is another one: $frac{4!}{4-frac44}=8$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 13 mins ago









          abc...abc...

          2,307531




          2,307531























              2












              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              share|cite









              $endgroup$













              • $begingroup$
                The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
                $endgroup$
                – Misha Lavrov
                5 mins ago
















              2












              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              share|cite









              $endgroup$













              • $begingroup$
                The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
                $endgroup$
                – Misha Lavrov
                5 mins ago














              2












              2








              2





              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              share|cite









              $endgroup$



              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$







              share|cite












              share|cite



              share|cite










              answered 9 mins ago









              trancelocationtrancelocation

              10.5k1722




              10.5k1722












              • $begingroup$
                The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
                $endgroup$
                – Misha Lavrov
                5 mins ago


















              • $begingroup$
                The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
                $endgroup$
                – Misha Lavrov
                5 mins ago
















              $begingroup$
              The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
              $endgroup$
              – Misha Lavrov
              5 mins ago




              $begingroup$
              The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
              $endgroup$
              – Misha Lavrov
              5 mins ago











              1












              $begingroup$

              We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



              Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



                Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



                  Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






                  share|cite|improve this answer









                  $endgroup$



                  We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



                  Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 10 mins ago









                  Chris CulterChris Culter

                  20.3k43584




                  20.3k43584






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3089195%2fare-there-any-other-shorter-expressions-for-8-by-manipulating-exactly-4-4%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Plaza Victoria

                      Image
                      Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l...
                      Read more

                      Puebla de Zaragoza

                      Image
                      Para otros usos de este término, véase Puebla (desambiguación). Heroica Puebla de Zaragoza Localidad De arriba a abajo de izquierda a derecha: Estrella de Puebla, Volcán Popocatépetl, Catedral de Puebla, Monumento a Ignacio Zaragoza, Estadio Cuauhtémoc, Angelópolis y Vista panorámica de la ciudad. Escudo Otros nombres: El relicario de América/ La ciudad de los Ángeles/ La Angelópolis Lema: Muy noble y muy leal ciudad de Puebla de los Ángeles Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en México Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en Puebla Mapa interactivo Coordenadas 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Coordenadas: 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Idioma oficial Español Entidad Localidad  • País   México  • Estado Puebla  • Municipio Puebla Presidente municipal Claudia Rivera Vivanc...
                      Read more

                      Musa

                      Image
                      Para el género de plantas, véase Musa (planta). Apolo y la Nueve Musas En la mitología griega, las musas (en griego antiguo μοῦσαι « mousai» ) son, según los escritores más antiguos, las divinidades inspiradoras de las Artes: cada una de ellas está relacionada con ramas artísticas y del conocimiento. Son hijas de Zeus y de Mnemósine, compañeras del séquito de Apolo, dios olímpico de la música y patrón de las bellas artes, quien tuvo romances con cada una de ellas, dejando descendientes. Bajaban a la tierra a susurrar ideas e inspirar a aquellos mortales que las invocaran. En la época más arcaica eran las ninfas inspiradoras de las fuentes, en las cuales eran adoradas. Finalmente, alrededor de los siglos VIII-VII a. C. [ 1 ] ​ prevaleció en todo el territorio de la Hélade la adoración de las nueve Musas, que son Calíope, Clío, Erato, Euterpe, Melpómene, Polimnia, Talía, Terpsícore y Urania. El culto a las musas era originalmente de Tracia y Beocia, y fueron de vital impo...
                      Read more